{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "import warnings\n",
    "# Ignore numpy dtype warnings. These warnings are caused by an interaction\n",
    "# between numpy and Cython and can be safely ignored.\n",
    "# Reference: https://stackoverflow.com/a/40846742\n",
    "warnings.filterwarnings(\"ignore\", message=\"numpy.dtype size changed\")\n",
    "warnings.filterwarnings(\"ignore\", message=\"numpy.ufunc size changed\")\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "%matplotlib inline\n",
    "import ipywidgets as widgets\n",
    "from ipywidgets import interact, interactive, fixed, interact_manual\n",
    "import nbinteract as nbi\n",
    "\n",
    "sns.set()\n",
    "sns.set_context('talk')\n",
    "np.set_printoptions(threshold=20, precision=2, suppress=True)\n",
    "pd.options.display.max_rows = 7\n",
    "pd.options.display.max_columns = 8\n",
    "pd.set_option('precision', 2)\n",
    "# This option stops scientific notation for pandas\n",
    "# pd.set_option('display.float_format', '{:.2f}'.format)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "def df_interact(df, nrows=7, ncols=7):\n",
    "    '''\n",
    "    Outputs sliders that show rows and columns of df\n",
    "    '''\n",
    "    def peek(row=0, col=0):\n",
    "        return df.iloc[row:row + nrows, col:col + ncols]\n",
    "    if len(df.columns) <= ncols:\n",
    "        interact(peek, row=(0, len(df) - nrows, nrows), col=fixed(0))\n",
    "    else:\n",
    "        interact(peek,\n",
    "                 row=(0, len(df) - nrows, nrows),\n",
    "                 col=(0, len(df.columns) - ncols))\n",
    "    print('({} rows, {} columns) total'.format(df.shape[0], df.shape[1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Model Bias and Variance\n",
    "\n",
    "We have previously seen that our choice of model has two basic sources of error.\n",
    "\n",
    "Our model may be too simple—a linear model is not able to properly fit data generated from a quadratic process, for example. This type of error arises from model **bias**.\n",
    "\n",
    "Our model may also fit the random noise present in the data—even if we fit a quadratic process using a quadratic model, the model may predict different outcomes than the true process produces. This type of error arises from model **variance**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Bias-Variance Decomposition\n",
    "\n",
    "We can make the statements above more precise by decomposing our formula for model risk. Recall that the **risk** for a model $ f_\\hat{\\theta} $ is the expected loss for all possible sets of training data $ X $, $ y $ and all input-output points $ z$, $ \\gamma $ in the population:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "R(f_\\hat{\\theta}) = \\mathbb{E}[ \\ell(\\gamma, f_\\hat{\\theta} (z)) ]\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "We denote the process that generates the true population data as $ f_\\theta(x) $. The output point $ \\gamma $ is generated by our population process plus some random noise in data collection: $ \\gamma_i = f_\\theta(z_i) + \\epsilon $.  The random noise $ \\epsilon $ is a random variable with a mean of zero: $ \\mathbb{E}[\\epsilon] = 0 $."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we use the squared error as our loss function, the above expression becomes:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "R(f_\\hat{\\theta}) = \\mathbb{E}[ (\\gamma - f_\\hat{\\theta} (z))^2 ]\n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With some algebraic manipulation, we can show that the above expression is equivalent to:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "R(f_\\hat{\\theta}) = (\\mathbb{E}[f_\\hat{\\theta}(z)] - f_\\theta(z))^2 + \\text{Var}(f_\\hat{\\theta}(z)) + \\text{Var}(\\epsilon)\n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first term in this expression, $ (\\mathbb{E}[f_\\hat{\\theta}(z)] - f_\\theta(z))^2 $, is a mathematical expression for the bias of the model. (Technically, this term represents the bias squared, $\\text{bias}^2$.) The bias is equal to zero if in the long run our choice of model $ f_\\hat{\\theta}(z) $ predicts the same outcomes produced by the population process $ f_\\theta(z) $. The bias is high if our choice of model makes poor predictions of the population process even when we have the entire population as our dataset.\n",
    "\n",
    "The second term in this expression, $ \\text{Var}(f_\\hat{\\theta}(z)) $, represents the model variance. The variance is low when the model's predictions don't change much when the model is trained on different datasets from the population. The variance is high when the model's predictions change greatly when the model is trained on different datasets from the population.\n",
    "\n",
    "The third and final term in this expression, $ \\text{Var}(\\epsilon) $, represents the irreducible error or the noise in the data generation and collection process. This term is small when the data generation and collection process is precise or has low variation. This term is large when the data contain large amounts of noise."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Derivation of Bias-Variance Decomposition\n",
    "\n",
    "\n",
    "To begin the decomposition, we start with the mean squared error:\n",
    "\n",
    "$$\\mathbb{E}[(\\gamma - f_{\\hat{\\theta}}(z))^2]$$\n",
    "\n",
    "And expand the square and apply linearity of expectation:\n",
    "\n",
    "$$ =\\mathbb{E}[\\gamma^2 -2\\gamma f_{\\hat{\\theta}} +f_\\hat{\\theta}(z)^2]$$  \n",
    "$$= \\mathbb{E}[\\gamma^2] - \\mathbb{E}[2\\gamma f_{\\hat{\\theta}}(z)] + \\mathbb{E}[f_{\\hat{\\theta}}(z)^2]$$\n",
    "\n",
    "Because $ \\gamma $ and $f_{\\hat{\\theta}}(z)$ are independent (the model outputs and population observations don't depend on each other), we can say that $\\mathbb{E}[2\\gamma f_{\\hat{\\theta}}(z)] = \\mathbb{E}[2\\gamma]  \\mathbb{E}[f_{\\hat{\\theta}}(z)] $. We then substitute $f_\\theta(z) + \\epsilon$ for $\\gamma$:\n",
    "\n",
    "$$ =\\mathbb{E}[(f_\\theta(z) + \\epsilon)^2] - \\mathbb{E}[2(f_\\theta(z) + \\epsilon)] \\mathbb{E}[f_{\\hat{\\theta}}(z)] + \\mathbb{E}[f_{\\hat{\\theta}}(z)^2]$$          \n",
    "\n",
    "Simplifiying some more: (Note that $\\mathbb{E}[f_\\theta(z)] = f_\\theta(z)$ because $f_\\theta(z)$ is a deterministic function, given a particular query point $ z $.)   \n",
    "\n",
    "\n",
    "$$ =\\mathbb{E}[f_\\theta(z)^2 + 2f_\\theta(z) \\epsilon + \\epsilon^2] - (2f_\\theta(z) + \\mathbb{E}[2\\epsilon]) \\mathbb{E}[f_{\\hat{\\theta}}(z)] + \\mathbb{E}[f_{\\hat{\\theta}}(z)^2]$$ \n",
    "\n",
    "Applying linearity of expectation again:\n",
    "\n",
    "$$= f_\\theta(z)^2 + 2f_\\theta(z)\\mathbb{E}[\\epsilon] + \\mathbb{E}[\\epsilon^2] - (2f_\\theta(z) + 2\\mathbb{E}[\\epsilon]) \\mathbb{E}[f_{\\hat{\\theta}}(z)] + \\mathbb{E}[f_{\\hat{\\theta}}(z)^2]$$   \n",
    "\n",
    "Noting that $\\big( \\mathbb{E}[\\epsilon] = 0 \\big) => \\big( \\mathbb{E}[\\epsilon^2] = \\text{Var}(\\epsilon) \\big)$ because $\\text{Var}(\\epsilon) = \\mathbb{E}[\\epsilon^2]-\\mathbb{E}[\\epsilon]^2$:\n",
    "\n",
    "$$ = f_\\theta(z)^2 + \\text{Var}(\\epsilon) - 2f_\\theta(z) \\mathbb{E}[f_{\\hat{\\theta}}(z)] + \\mathbb{E}[f_{\\hat{\\theta}}(z)^2]$$           \n",
    "\n",
    "We can then rewrite the equation as:\n",
    "\n",
    "$$ = f_\\theta(z)^2 + \\text{Var}(\\epsilon) - 2f_\\theta(z) \\mathbb{E}[f_{\\hat{\\theta}}(z)] + \\mathbb{E}[f_{\\hat{\\theta}}(z)^2] -  \\mathbb{E}[f_{\\hat{\\theta}}(z)]^2 + \\mathbb{E}[f_{\\hat{\\theta}}(z)]^2$$\n",
    "\n",
    "Because $ \\mathbb{E}[f_{\\hat{\\theta}}(z)^2] -  \\mathbb{E}[f_{\\hat{\\theta}}(z)]^2 = Var(f_{\\hat{\\theta}}(z))$:\n",
    "\n",
    "$$ =  f_\\theta(z)^2 - 2f_\\theta(z) \\mathbb{E}[f_{\\hat{\\theta}}(z)] + \\mathbb{E}[f_{\\hat{\\theta}}(z)]^2 + Var(f_{\\hat{\\theta}}(z)) + \\text{Var}(\\epsilon)$$ \n",
    "\n",
    "\n",
    "\n",
    "$$ = (f_\\theta(z) - \\mathbb{E}[f_{\\hat{\\theta}}(z)])^2 + Var(f_{\\hat{\\theta}}(z)) + \\text{Var}(\\epsilon) $$                    \n",
    "$$= \\text{bias}^2 + \\text{model variance} + \\text{noise}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To pick a model that performs well, we seek to minimize the risk. To minimize the risk, we attempt to minimize the bias, variance, and noise terms of the bias-variance decomposition. Decreasing the noise term typically requires improvements to the data collection process—purchasing more precise sensors, for example. To decrease bias and variance, however, we must tune the complexity of our models. Models that are too simple have high bias; models that are too complex have high variance. This is the essence of the *bias-variance tradeoff*, a fundamental issue that we face in choosing models for prediction."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Linear Regression and Sine Waves\n",
    "\n",
    "Suppose we are modeling data generated from the oscillating function shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "from collections import namedtuple\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "np.random.seed(42)\n",
    "\n",
    "Line = namedtuple('Line', ['x_start', 'x_end', 'y_start', 'y_end'])\n",
    "\n",
    "def f(x): return np.sin(x) + 0.3 * x\n",
    "\n",
    "def noise(n):\n",
    "    return np.random.normal(scale=0.1, size=n)\n",
    "\n",
    "def draw(n):\n",
    "    points = np.random.choice(np.arange(0, 20, 0.2), size=n)\n",
    "    return points, f(points) + noise(n)\n",
    "\n",
    "def fit_line(x, y, x_start=0, x_end=20):\n",
    "    clf = LinearRegression().fit(x.reshape(-1, 1), y)\n",
    "    return Line(x_start, x_end, clf.predict(x_start)[0], clf.predict(x_end)[0])\n",
    "\n",
    "population_x = np.arange(0, 20, 0.2)\n",
    "population_y = f(population_x)\n",
    "\n",
    "avg_line = fit_line(population_x, population_y)\n",
    "\n",
    "datasets = [draw(100) for _ in range(20)]\n",
    "random_lines = [fit_line(x, y) for x, y in datasets]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e51c2ac908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(population_x, population_y)\n",
    "plt.title('True underlying data generation process');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we randomly draw a dataset from the population, we may end up with the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e5276c94e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs, ys = draw(100)\n",
    "plt.scatter(xs, ys, s=10)\n",
    "plt.title('One set of observed data');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose we draw many sets of data from the population and fit a simple linear model to each one. Below, we plot the population data generation scheme in blue and the model predictions in green."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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CIAiCX1iZVUBxhT7KvbIVjnJBJF1BEATBD3hVlZ/W7gNgcI8E2sSGtHCPjk8kXUEQBOGst0kpoqjcAcBlQ9u3cG9OTCRdQRAE4aymaRo/rc0DoE+nGNrGt75zuTVE0hUEQRDOatn7yth32ArAJUNSWrg3JyeSriAIgnBW+2mdPsrtkBRO13aRLdybkxNJVxAEQThr7TtkZVtuKQCXDk1pNTWWT0QkXUEQBOGs9fN6fZSbEBVEvy5xLdybUxNJVxAEQTgrFZXbWZ99GICLh6RgMLTuUS6IpCsIgiCcpRatz0fTIDwkgOG9Ek/7+emHN3LXon9T5apqgt4dn6khjWRZbgvMBM4BKoGpiqK83pQdEwRBEIQTsTncrMwqAGDMgLaYTcYGP1cp3cGL654no3ATjw15nBBzCC6qm6qr9ZxypCvLsgTMA7KBGOAi4H+yLA9v4r4JgiAIwnEt31yA0+0lwGTg3H5tGvScfGse9y75P66efymDEoewdlwGN/f8Z7MuvmrISHcIkAyMVxTFC2yTZXkYUNykPRMEQRCE4/CqKr9tygdgeK9EQoPMJ21fZCvitfRpfK18wa29/sXav2cQbolojq4eoyFJtz+wDZgqy/I49OnliYqifNSQDUiShKGRzhzXnCQ/G06Wn4q/xOIvcYCIpTXylzhAxNKY0ncWU1LpBGDs4HYYjcfvR6Wrkhnpb/B+1jtc2/V6Vt+0kfjg+HptmjuWhiTdaOA8YAmQAgwEfpZlOUdRlBWnenJMTEijD90jI1tnIesz4S+x+EscIGJpjfwlDhCxNIbf0jMA6C/H01s+dgGVw+NgxoYZTFk1hYs7X8ymOzbRIar+XYc8qodZGbOYumoqGXdmEBkZ3ix9b0jSdQKliqK86Pv/almW5wJXAadMuiUl1Y060o2MDKG8vBpV1RrnRVuIv8TiL3GAiKU18pc4QMTSWHIOVpK9Vy+GcV6/ZEpLj6w89qgevsiew9T1k+kT15dvr/qe7jE9QKO2naZpzN/9HU+teJxKVwUpYe0xGUyNGkt09IlrPzck6SpAiCzLJkVRPL7HjECDhq+apuH1NqRlw6mqhtd7dh+0NfwlFn+JA0QsrZG/xAEilj/qF18xjKSYYLq3j8Lr1dA0jYU583lx3fPEByfw7tjZDEocAlCvf8vyf+eJFY9wsPogEQHhvH7eTLpEdybIFIRDrW6WWBqSdBcDZcBkWZbHA4OBq4ELm7JjgiAIglBXmdXJhuxCAMYMbIcELM1fwqS1E1DReGHkFM5rd8ExpzTTD2/kyZWPsaN0O2ZDAP8b/gKdI7sydcNEimyFZHbIaLYYTpl0FUWxy7J8LvAmUIi+kOpeRVHWNnHfBEEQBKHW7xn78aoaIYEmguIOcO2CuzhQtZ/HhzzNFZ3+gkGqfy5zZ6nC/1Y/yeqDK5GQuLf/gwxLHsH09GnsKM0mNbwDpfYSNJpvtN6g4hiKouwGLm7ivgiCIAjCcbk9XpZmHMRqyCc/5lvu+m0nDw16jBvkcZiN9S8ZOmDdz8R1E/ghZwFocHPPW7m805XMzHyLWVvfpWuUjNVZSbW7Gpfqwu11Aye/7KixNCjpCoIgCEJL+j49g5XayxQGb+K+zvfzn0FfEGQKqtem1FHCKxtf4pPtswGJSzpczi09buXj7bO59aeb6BnbC4fbToWzArfqRindwXkp5xNsDqba7m6WOETtZUEQBKHVKrIV8eSKx7hv41UEaTE8kPgVjwx7qF7CrXJXMW3DFAZ80os52R8zJHEoH138GcGmYG79eRwl9mK8mocSezFuzc3u8l0MSRrO3CvnM6LNiGOmpZuSSLqCIAhCq2N1VTJl/URGfj6Qsio751jfQHaO4/LB3WrbuLwu3t/yDv0/7sHMzW/SMaIzM8a8R+eortyx+FbyrXkYJCOHbIdwel3srcilb1w/Pr30S5JDk7n8u4t4auUT7C7d3WxxiellQRAEodVweBzM3vo+b2S8yvkpY1j8t+X8sMTKBq2QtnEhdG0XiVf18u2ur3l+zbM4vA7CAyJ4bPCTZJds4/4ld9MnLo1AYyAHqvZj99g5YM2nW3R3Hh44ngV7vuPaBVeioWGQDEQERBIXHKdXpGgGIukKgiAILc6jevhyx2dM2ziZ3nF9mXulXtiitNLBJiUHgAsGtGXxvp95dtWTlDhKMEpGxg9+kiJ7EU+vGk+vmD6EBoSxr3IvVreVak8VqREdeHjgeH7KWchNP15Xm2wDDBbcXhdp8f0IDwynyulqljhF0hUEQRBazNGFLd4b+yEDEwfX/nxp5gFUTcMWpPDCrufYW5mDqnq5J+0+JEnipQ2T6R7TnShLNHsqdlPhrMAgGUgKSeahgY+yeO8ibv/l5iPJVgrAo3oYmjScSzpcxpL8Rbi8zZNwQSRdQRAEoQVomsay/b+ftLCF2+NlXuYqNgW9j9WyG0OZys09/qlXndryNh0jOxEfnMCusl3Y3NUYJAMxgTHcN+Ahlucv5e5f/12bbM2SGVVTGZo8nDHtx/JZ9ifMynqXyMBINE2jgUUW/zCRdAVBEIRmtenwBiaunUBB9UEeH/w0l3e66pgVxHsrcnlw0ROsMf4GGlzW/gr6JfZhVta7JIUmkxySzM5SBbfqwiAZCQsI47/9H2D1wZU8tPTe2mRrksxomsqw5JGMajuKz3fM4bPtn+LwOthbmUtqRAekZkq4IJKuIAiC0EyU0h1MWvccmwszeHjQeG7oNg6ToX4aKrQV8vKGyXypfI7HA1GeHqRFD2Vr6S/kV+eQHNqGnaUKmqRhQCLQGMTdaf9l46F1PLHi0SPJ1pfehieNZEjyUL7YMYcSRzEur5Mc6x46hHdkUOIQsoo3Y/PYMBHcLPtAJF1BEAShSeVb83hpw4v8uu8X7km7n5kXzjqmsEWls4K3Ml/nvS1vYzYEkBrSGe/hPhw0LyOXpSSFJLOlaDNGg0G/T7tk4N997ibzcAYT1jx9bLJtM5K0+P58pXxOmasUl+piW3EWXaNkesX2QSnNJq8qD7NkQtXUZtsXIukKgiAITaLIVsRr6dP4WvmCW3v/m7V/zyDcElGvjd1jZ/bW93l140sEGM3EByVwjXwdczK/o9L8OxHGeA7ZFUpdBZgMRryayq09b2dbyVamrp9Ym2yNGDFIBoYlj6B7TA/m7vyaCmc5btXNlqJMekb3IsQcSm5FDpJkwKt6kSSJ63uMIz4knnKXrVn2iUi6giAIQqOyuiqZkfkGH2S9y7Vdr2fFjRuID46v16bmEqEX1z2HJElYTBZu7DaOtQVr+GrHl7htkdhMuWCqwmzUVxz/vfst7CxVeD3jFT3ZYsAo6cl2aNJwOkV1Yf6uuVT6ku3mokx6xvYmwBDArvKdmI1mPKoHk8HEv/rcxWNDniQiMKxZK1KJpCsIgiA0CofHwQdb3+PNjOm1hS1SwtvXa6NfIrSA59c8g81jw6k6ua7r31HKspm762u6R/cgsyoT1ViEETMabv7S6QZyKnJ4b8vbqKi1ydYoGRmcOIyUiBQW7p5PhavCl2w30yu2D/slA0ppNsGmYDyqB6Nk5L7+D/HAwEcINAW2yD4SSVcQBEH4Q2pGrS9teJE+8Wm1hS2Otnz/UiasfppD1Qexe+xc2elqiuyFfJ8zj76x/ahwlLPx0AZU1YgquRkUORZDSBkfb5+tJ1vfOVuTwcTAhEEkhiazKPcnyl3luDT9nG2PmF7kVOxme+lWIgP06lWqpvL4kKe5p999xyzcam4i6QqCIAhnRNM0vt8zjxfXPU9CcCLvX/RRvcIWNTIL03luzTNsL9mK2+vmvHZjcGtuFu/7mUGJQ7C77aw/tAZJMmBz24l1D8AhlbC+YiFqhT6yNUkmzAYzafEDiAuOY2neb5Q7y3GoTnaWZtM1WmZn2U62l2wlJigWm9uGV/Py/IjJ3N7njmadQj4ZkXQFQRCE06JpGov3LOaRRY+haRoTR07l3Hbn1ytsAbC7bBeT1k1gxf5lgERafH/CAkJZeXA5Q5OGoWoaqw+uQkXFo3oZ3eY8Nu7dTYF5FUg152xNBBgC6BufRqQlkjUHVpEc1hab18aeij10jujMrvKdKKU7iA2Ko6D6IKqm8vK5r/P37jcf06eWJpKuIAiC0GCbDm9g4roJFNoPMX7QU1za4cpjRpEHqw7w0oYXWbD7OyymQDpGdqJtaDtWHljO0OQRBBgCWHVgBV5NBTQGJw6l1FHCz3t/9F2+I2HEhMVkoVdsb0LNoWQc3kRcSAJVnir2W/PoEN6R3IoccitzSQxOIr8qD9CYeeEHXN3lmpbYNQ0ikq4gCIJwSjtKs3lx3fNsLszg0SHjuWfEXVSWO/B6tdo2pY4SXk9/lU+2zSYkIJS4oAR6xPZg1YEVJIYkERYQzsoDy1E1LxIG+salUeEsZ2n+ElT0ZAtGTFIAafG9sZgsZJdsJyoomgpXBZqk0S4shXxrPoW2wySHtiXPuhfJYGDOpV9xYerFLbZ/GkokXUEQhDNgtbmwu7xEhARgMRtbujtNJt+ax9T1k/gtbxH/6fcAMy+cRagluN6CpGp3Ne9unsGMzNcJt4QTYg6lX3x/1h5cjcvrJiYojhX7l6FqKibJTI+YXlidVtYUrELVVCQkvTay10SY2pbEqDByrTmEmcModZYgSRKJIYkcth3GYgykbVg79lXmEhccz9wrFzKq7TktuIdOj0i6giAIDVBld5O9r4wdeWUoeeUcLK6u/VmQxUhEiIU2sSGck5ZMzw7RGFrZucTTVWQrYvqml/hm55cnLGzh8rr4aOuHTNswmWBTMBIGukX3IP3wJtyqm+TQtqw8sBwNFYsxkPbh7aly29h0aCMqXj3ZGgIINFqIlNpS6XbjMBZTpTkosRdjwEBMYCzlzjLahaXQNrQd+6x76R7dgx//+utxF221diLpCoIgnITHq7JoQz4LVuXich+/XKDd6cXutHGo1MamnUXERwVxfr82jOiTREiguZl7/MdUOiuYsfkNZme9d8LCFqqm8lnWZ4xf/DgSEg63nV6xvdlWvBWX1037sFRWHViBpmmEmEOIC47H4XaytTgLr6Yn2wCDhUBjIO0j2uPyesgrOYxm0HBIZbhVC2EB4ZQ4iukW3YMQcwj7KvfSJy6N2ZfMoVds7xbaO3+cSLqCIAgnkL2vjE8XKRSU6CUCjQaJjsnhyCmRyClRRIdZqKhyUV7tpNzqIn1nEbsPVFBYZueLJbuZtzKXG8d0YWTvJJrr1nFnqm5hiwtSLjxhYYvf8hbx/NpnqXJbKXeU0yuuL27VjdvrplNkZ9YWrAY0wgLCCQ8Ix+31sKtsZ22yDTQEYjEFkhzaBpfqotRRitVhxy6VYNGiCTIGUWwvol/8AAqqDpJdso2BiYP5/PJv6BIlt8zOaUQi6QqCIBzF6fby8c8Ka7YdAvR0ObpfG/56TkdCg+qPXJNiQmr/ffGQFPIOW1mSvp+12w7jcHmZ/eMOtuwu4bbLuhMd3ZxRNIxH9fDFjjlM2zCZvvH9+PaqhXSL7n5Mu3UFa3lh7bPsrcjB6XHRJbYzmgZe1UPniC6sP7wWDY1ISxQWowWP18O+yr21yTbIGIzFaCExJJFqt40qt5Uql5UyZzmBWiQSJjwGK8MTh7O7fBebDm9gePIo5v3lR9pHpDb/jmkiIukKgiDU4XB5eP2bLezIKwegfWIYt1wk0yEpvEHPT0kI45+XdOfqUR2Z/dMOtuwpYdPOIvYcrOCBGweQGt88t5A7Fb0c4/xTFrbYXrKNSWufY9Ph9RgkI9GWaBwmB5qmIUd1812DC9GBMYCGpkFB1UE8mgcJiWBTCBajhZigWKpdVdg8NspdpVS5qogNisOAATd24jxpeEP3serACs5tdz4/X7OEpNDkZt4rTU8kXUEQBB+bw8OrX2ey50AlAFeP6sBlw1IxGE5/ajgi1MJ91/ZhaeZBvvxtF+VVLp59bw3jxnblgv5tG7vrDaZpGkvzlzBp3XNonLiwxb7KvUxdP4lF+34mzBxGsCkEs9GM0WikW2R3/TIfTSUuKB6n14lH9VDuLKtNtqGmMAKMZqICo6l0VuDxuqlwlePwOIgOjKZaqsarekiVRpCnplNkTufipEuYdu7rxAUCfEewAAAgAElEQVTHtdDeaXoi6QqCIKCvTn75y0z2HbICMO7Crlww4I8lR0mSOK9fG7qlRPLu99vZd8jKnEU7qba5uWJEarNXS9p0eAMT106goPogjw9+mss7XXVMYYtCWyHTN73EV8rnxAbFYTYEYDFZkJDoEimzJH8xu8p2khiaiNVZhd1tx+q24tHcSEiEmcMIMFgICwijwlWBV/VQ6a6k1FFKuCUCu8eOxRTEX9pew8+5P5OrriTJM5x3L3+LwZ07NOv+aAkNSrqyLD8CTARcdR6+RFGUFU3SK0EQhGZkc7iZ+lkG+4uqkIB/XNKNc/o23tRmUkwIT948gBnzt5G5s4h5K3OxOT1cf37nZkm8dQtbPDxoPDd0G3dM4X+rq5K3Ml9n1pZ3iA9JAPQbxQeZAuke1YPf8n9lb2UuCcGJVLoqqXJWUeW24lE9AESYIwgwWgg0BdYWsqhyW6l0VRJiDsbldREfHM/Y1ItYuGcBC3K+o7v5QpLKbqJrYiKDOqU2+X5oDRo60k0DnlAUZVpTdkYQBKG5qZrG+wuz9YQrwb8u68GwXomNvh1LgJFnbh/CpA/WsVEpYtGGfGwOD/+8pNsZTV83RF7lPl7a8GK9whZBpqB6bRweB7O3vs/r6S8TExSHR/WgairB5mB6xPRiSd5ift77IwkhiZQ7y6h0VGBX7bXJNtISRYAhAJPBRKWrgkBzINWuKuweGwGGAGweG12iZDpHdmb+7u/Ircjhxu43c3vnx5j6yXYAxg5u1+pqJDeVhibdfsDspuyIIAhCS/hlXR6Zu4sBfUq5KRJuDbPJyN1/7cWshdmsyjrEyqwCjEaJWy6SGzXpNKSwhUf18LXyBVPWv0BoQBhOjxO36iLQFESvmD4szV/CjznfkxCSiEctptxRhlN11ibb2KBYDJoBo9FEuaOc6KBobG4bLq8Ls9GMS3UxJGkYsUGxzNv9LVuLt/CPnrfz+JCnCTGHMHP+VgDiIgMZ1C3+mBj81SmTrizLwUBX4D5Zlj8FyoCXFEX5oCEbkCQJQyPdUanm22BTfStsTv4Si7/EASKW1qip49ixr4xvlu0BYFivRMYMbNtkI66aGMwmI/+6ogeBAUZ+23SAZZkHiQqzcPU5Hf/wNiqdFbyV8Qazst7lb/INrL5p4zGFLTRN44ec73lhzQS8qpdqtw2T0YzJaCItrh8rDixnYc58EkMScXgclNpL8GpeHF4HALGBsRglIwajgXJ7OZHGKJxeB0X2QowGIxoal3S8DEmT+D5nPiaDif/r9x8eHvQYwWZ95XZBSTUbsgsBuHx4KgEtWEazud8rDRnpJgCrgLeBa4AhwPeyLBcoivLTqZ4cExPS6AdxZGTIqRudJfwlFn+JA0QsrVFTxFFa6eDt+dvQNGiXEMaDfx9AoKXp15bWxHLvDQNwejRWbj7IvBW5JCeEc8mw1DN6TbvbzowNM5i6eiqXdL6E9DvTSY089rV+z/2d8b+Op9BWiMPjwIABJI2hbYewKn8VC/bMIzE0EaNkpMRegooXp9cNQEJwAkaDEY/mocJRQWRgJE6vk1KHXhvZbDBzc5+bKawuZMHO+ViMFp4c9SSPjXyMQFNgvX58vGgnGhAbEcgVo7tgNrX8vW6b670iaZp26lZHkWX5DSBAUZQ7T9W2uLhKa8yRbmRkCOXl1ajq6fe7NfGXWPwlDhCxtEZNFYdXVZkyJwMlrxyL2cj/bhtEcmzTfugeLxa3R+XlLzLJ3leGJMF/r+nDALnhl8t4VA+fZ3/K1PWTSYvvx5NDn6FbzLGFLTILM3hhzQSyS7ZjNpixuW04vU4uSBlDRuEm9lftJz4ogVJ7CQCapOFWa5JtIgYkHF4ndreNUEsoZfYyTEYTLq+LSEskt/T8J9tLtvF73hKCTEE8MOhh7kq7B4vRckxfisrtPPb2GryqxrixXRk7qN2Z7M5G0xTHWHR06AlHmg2ZXu4PjFUUZXKdhwMBW0M2rmkaXm9DWjacqmr1bid1NvOXWPwlDhCxtEaNHcdP6/JQfMUvbr20GwlRwc22n+rGYpAk7rm6N1M+Sye/sIq3523lkRv70blNxMlfQ1NZuGc+k9e/oBe2GHuksEXdOPaU72LyuomsPLCMqMBobK5qvHg5t+357Cjdwfc584kNisOEiRJ7MZoEHtUNGiQGJyFpEjaPnqADTRbcqhur04oXleSQeP7R83aW5i1hRuabBJmCeWb4c9zW6w4CjAHH9KXGD6v34VU1woPNjOyd1GqOz+Z6rzRkLqUKeFaW5d3At8B5wA3A6KbsmCAIQlMorrAzf2UuAKP6JDG4e0KL9ic40MQD1/Vl0iebKK5w8Oa3WTzzj4FEhwce07ahhS0Kqg4ybeMUvt8zj6SQZOweB46qg4xoM4p8ax4/7f2B6MAYzJKZElsxksFQm2zbhLRB06DKbcWtujEZTLhVF6rbixcvHSM6c2uv21mQ+y1T1k0k1BzGCyOncFP3f2A2nvzmDuVVTlZsKQBg7OAUv74l4omcMukqirJTluXr0K/T/QjYD9yqKEp6U3dOEAShMWmaxpxFO3G5VcKCzfztvM4t3SUAIn3VqyZ+sonKahdvzM1i/E396yWlhhS2KHOU8kbGdD7Z/iEpYSk43HbyrHsZnDSUEnsxv+5bRFRgFGYpgDJ7KZLBgBcvqF7ahLRD01S9oIWmIgEu1Y1H8+DVvPSN68eN3cbx0bYPmLD6aSIsEbx07itc1/XYa35P5Jf1eXi8KiGBJs7r16Yxd+FZo0F7SlGU74Hvm7gvgiAITSp9ZxGb9+jnLa8/v/MxNy9oSW3iQrnjip68MXcL+w5bmf1jNnde2ROlbMcpC1tUu6t5f8tM3t78Bm1DU3B6HORU7KFfwkBcXgfL838nwhKBxWChzFGOwSDVJtt2oSl4VZUyZykaGl7Vi9dXylHVvJzT9gIu73AVMza/xtOrHifCEsmr573BHcNuo6Lc3uAp2YoqJ79nHADgggFtCWqGRWut0Z8zakEQ/nTsTg+f/boLgO7toxjWs+muxz1TaV1i+evojsxdlsPSHVn8Yp+MYl99wsIWbq+bT7M/4pWNU4gPTsTpdbGnYhfdo3sSYApg3aHVhJrDsBgDqXBWYDAYUPGiqpAS2h636qHIXoRBMuDyulA1b+1U9RWd/sLINqN4ddM0nip4jKjAKKaf9xZXdf4rAWYTRsPpTQ0vWL0Xl1slyGJizMCWXTzVkkTSFQThT2HeilzKrE5MRombxnZttRWQBvUJ5p2dc9hk/ZnUgkt476JfGdGj/jW8qqYyb/dcJq97gWBzMC7VxZ7y3aSEpRATFMuaglWEmEIINAZS6arAKJlQUVFVldSwDri8bg7bDmE0mHCrblRNX+0aYAxgXPdb6BrVjVc2TuGXvT8RGxTLm+fP5LJOVx4znd1Qh0ttLM88CMBlw9q3qhmG5iaSriAIfi/vsJVfN+UDcOnQ9vXugdtaVDormLH5DWZnvcfVna+je85sig6b+OyXfDolJpIYHYymafye/ysvrJ2Aw2PH6XFw2HaI+KBEUmNTWXlgOfnWPIKMQVjdVoySPhr1ah46hHfE6XFysPoAZoMZj+bB5dHL6YeaQ7mz7z2EmkJ5LeMV3KqL+OAEpo6ezsUdLj3jZFvj2+U5eFWNqDALY/7gTSTOdiLpCoLg975eugdNg/ioIC4b1r6lu1OP3WNn9tb3eTNjOhekXMjivy0nJbw9JWkOJny4gSq7mzfmbuGSi1Smpb/Afms+BsnAwaoDRAfGMCxpBCsOLKPQfohAYxDVnqo6ydZLx/DOOD128q15BBgteDUVt8eGhkZsUBwPDngEq8vKm5mvARpJIck8Pew5xra/uFFmA3ILKtmwQ68+ddXIDi1afao1EElXEAS/lr23lG25pQBcO7oTZlPr+ND3qB6+2DGHaRsm0ze+H99etZBu0UcKW8REBPJ/f+nFs18tYIHtEz7/cQ/JEXEUVB0kNCCMUW1Hs2L/MlYdXIHFEEiVx1ov2XaK6ILdXc0+a66vSIWE3ZdsU8LaM37I0+wo2c7EdRMwSkbahaXw1NBnuSBlbKNNvWuaxjdL9TKbSTHBjOjd+s6jNzeRdAVB8FuapvHNshwAUhPDTqvaU1NRNZUFu+fx4vrnSQxO4v2LjhS2qCvfmseM3ZPYGPEjkiOKKm8ZeeUOzml3HqsPrGD5/mVYDBaqPFY8kn4TAq/mpXNEF6zOKnIr9mAxWjBgwO6xo6HRI7onTwx5hqX7l/Dw0nsxGcx0iujCk0OfPe71vn/Utr2lZO8rA+Ca0Z0wNlZ5wrOYSLqCIPit9J1F5BZUAnDtuZ1adPGUpmks2rOIRxeNBw0mjXzpuImuyFbEa+nT+Er5nNTwjji91WB2EOfqS6kpm6X5SwgyBmL32msXQHk1L10iu1LpqCSnYg9moxmjwYTD60BDY2jScB4c+Cjzds3l34v/SYAhgG7RPXhi6DOMajO6SfaLqh4Z5XZqE06/LrGNvo2zkUi6giD4Ja+q8u1yfZTbMzWKHqnRLdaXTYc3MHHdBArth3h88NNcmnrlMYnO6qrk7cw3eT/rHTpGdMTmtrO9dBvD24wkozCdYm0zkhqAqnqwaXoVXj3ZylQ4ytldvguzwYzJYMLpdSIhcVHqpdzZ524+2j6LW38ah8lopk9cGo8PfprhbUY2acxL0veTd7gK0Kf1W+tq8eYmkq4gCH5pVdYhCkr05HTNuZ1apA87SrNrC1s8OmQ894y4i8pyR72CEg6Pg4+2zeK19FdoF5aCy+tiS/EWhiQOJbt0OysOLCPIGISGiiY5AVBR6RzRlQpnObvLd2KQjJgMJlyqC6Nk5O/dbuaartfxzuY3ueWnGzAYjPRLGMCjg55gaPLwJo+7tNLBXN8XnqE9E5BTopp8m2cLkXQFQfA7Lre3tr7yoG7xpCaGN+v28yr3MXXDJJbk/cp/+t3PzAtnEWoJrldJyqt6+XrnF0xdP4mYoBg8Xg9bijIZkDCQ3IpcVh9cSZApGFVTsXns+pMkjVBvO+xSObsrdmLA4KuN7MZksPDffg8wss05vJ7xCrf/cjMa0D9xEI8OepxBiUOaLf45i3fidHkJCTRxw/ldmm27ZwORdAVB8DtLMw9SZnVikKRGuTl8QxXZipi+6SW+2fklt/b+N2v/nk64pf4dgzRN48echby47rnaSlBZxVvoFduHIlshGw6tJ9AYhIaG3aOP1DVUukbKlNhLKHHmgyYhaUZUyUuQMZinhz5H+4hUpm+axmc7PsGjehiUMJiHB42nf8LAZosf9PPoGbuKAbju/M6EhwQ06/ZbO5F0BUHwK26Pys/r9gEwvLdeVKKp1S1scW3X61l540bigo9dKb1071Ie/vkRyhzluL1O8qv20y2qGwHGALKKNmMxWtDQcHj1ka2GRtdImUJbITvLFSQkDJIRFS8mNZie9tu4oH8Kn+2YRZmjDIfXztCk4Tw88DH6xvdr8riPZnd6mLN4JwDdUiIZ2Tup2fvQ2omkKwiCX1m9tYDyKheSRJMXwjhS2OJVLkgZW1vY4mhZRZuZuG4Cuyt2YpICyKnYTYfwjrQPb49StgOLQU+2Tq9+zlZDo0ukTGH1oSPJFgMqKskhSUwZ9Sof/b6OldonKNtVjAFOzk05lwcGPkrv2D5NGvPJfLssp7bU5s0XyWLx1HGIpCsIgt/wqio/rtVHuYO7J5AQ1TSj3GMLW/xQr7BFjZyKPUxZ9wIrD6wgJiiG/Ip8kkKT6BjRidyKHMyGAD3ZqnWTbVcKqgrY5Uu2EhIaGp2jujB99FtkFqfzyPL7CDBb8BqriXH3pbftBib0v4Z2saFNEm9DZOWUsCR9PwCXD09tlaU2WwORdAVB8BsbsgspKncAeo3lxqZqKgv3zOfF9c+TFJJ8wsIWh6oLeHnjVBbs/o7k0GSK7UVomkaX6C7sKt2FSTKhoeFW9drHGhqdIrpwyFbArnJ9gVTN4/3jB/Ly6Nf4NW8Rt/x8I9FBMdg8NoaljOAf5/yXL+dbqbS7efWrTJ68eSAxEYGNHvepFJXbeXfBNjQgJSGUS4a0rlKbrYlIuoIg+AVV0/hhjT7KTescS7v4xhv1aZrG0vwlTFw3AQmJF0dNY3Tb846ZPi13lPFmxmt8sn02bcPaUemqwGP10DGyMznlu6lwluvJVnPrr4tGx/BOFNgK2FOxq16yPbftBUwcOYVvdn3B1QsuIymkDR7NQ1pcPx4Y8Aido/RVwUnXVTJlTgblVS5e+SqTx28a0Kx38XG5vbz1XRbVDg8hgSbuubo3ZpOoPHUiYs8IguAXNu8q5kBxNdC453I3HlrPX+dfzhMrH+G+/g+y6Nqlx1SSsrltvJ7+KkM/68/S/CXY3DZ2l+0iNbwDVS4r+8pz6yVbkOgQ1pFAYyA5lXtweZw1D/PXzn9j1Y0bkKNlLvn2fH7dtxgNSIvvxy/X/s5bY96tTbgAqYnh3H11L4wGiYISGy9/mUmV3U1z0DSNTxYp5B2uQgLuuLIncZFBp3zen5lIuoIgnPU0TWPhmr2AfoP6Tm0iTtq+IXaUZnPLTzfyr1/+wbVdr2fFDeu5otNf6iVbt9fNR9s+YOhn/Zi/ey4Or4PtJdtIDm2D0+sktyIHDQ0Pem1kCYn2YakEGALItebg8urTy5JB4l+972LZ9WsJCQjh4rnns+7QWiQk+salsfjaZbx2/gw6Rhy/yEfvjjHcemk3JGDfIStTPkunosr5h/fBqSzNOMCqrEMAXDWqA707xjT5Ns92IukKgnDW276vjNwCKwCX/8FRbl7lPv7z2538df7lDEsawdpxGYzrcUu9whaqpjJv11xGfjGID7Lew+6xsa14K7GBcah42Vu5V79pPCqgJ9t2YSmYDCb2WffiUfWRqNkYwKODnmTRNcsodZRwxXdjyS7ZjiQZ6BObxpLrV/HKeW+QGtHhlP0e3iuJf1/RA4MkcaComhfnpFNS4fhD++JkVm05yCe/6JcH9e0Uw+XDU5tsW/5EnNMVBOGs9/O6PAA6JofTrf2ZlRwstBUyfdNLzN35Fbf1voN14zIIC6hfyUq/ifxvTFw7AZu7mkqnlb2OXJJD22B1VZFv3YfGkRKPEhLJIW04VF1AvjUPCX2UHGwO4elhE+gbm8b0jJeZlTWTzlFd0dDoE9eX98Z+SJuw07/Z+9CeiQSYjcycv5XCMjuT52zioRv6Nfq1yss3H2T2D9moGiRGB9cme+HURNIVBOGstr+oqvZ+uRcPTjnta0MrnRXMyHyd2Vvf52/yDScsbLHx0Homrp3Avsq9eDQPh6oLSAxOwiAZOFC1v15bCYnEkEQOVx/mQPX+2mQbExzDlHNeJtoSy6ubpvHqxpfoGNkJj+alT2xf3r1wNkmhyWe4J3T9u8Zx7zV9ePPbLEoqnTz34QZuvkhmWM/GuZftovV5fLFkNwAp8aE8cH0awYHNt3DrbCeSriAIZ7VFG/IBiI0IpH/Xht8v1+6x80HWe7yVOf2khS2U0h1MWvccmw6vx2IIZH9VPrGBcRglE4dsBfXaSkjEBcVRZC+ioPrIz5JC2/DGBTOwBBuY8PtzHK4+TPvwVOxeO33i0njnwg9ICGm8G7z36hjDg9en8ea3WVTZ3bz3/Xa25ZYy7sKuBFnO7GNfVTXmrcxl4eq9AHRPjea/1/Qi0CzSyOkQe0sQhLNWRbWLtdv0hTwXDmyHwXDqUW7dwhZp8f357qofkaO7HdNuvzWfqRsm8UvuT0RYIii0FRJpicQkmSh2FNVra8BAdGA0JY4SCu2FtY93juzCmxe8S751H8+uehIvHhKCEql0VdAnLo2ZF35w3FF1Y+jaLpLnbh/M+wu3s31vGau3HmL3/gpuvlimR/uo05oRUPLKmLN4F/uL9Fv19eoYzbP/Goatuv4dk4RTE0lXEISz1u/p+/F4NYIsJkb2OXmd36MLW8y6+GMGJAw6pl2xvZjX0l/mix1ziA2KpdxZhkt1YTKYKHeW12trwECEJYJyZznFjuLax/vEpvHG+TPJLErnnt/+TbAphLigeDYXZ3BR+0uZMWYWsUFNf1P3yFALD16fxi/r8/h2WQ6F5XZe/iKTdvGhjB3UjiE9EjAZT7yetrjczldL97Bxx5EvEiN6J3Lrpd0JtJiwVTd5CH5HJF1BEM5KLreXJekHABidlnzCadOaxU+T1j130sIWVS4rMze/xbtb3iY2KBarsxKnx4HRYKLaXVWvrQEDYeZwKtzllDnLah8fkTyKl899g9/zFzPux7+RFJpM+/AOZBZuYmyHi/j6hi+RHJZmHR0aJIlLhrSnW0oUny5SyC2wkl9Yxawfsvlm2R56pkYTGxFITEQg0eGBFJfb2XOgkj0HK2rvRwzQPiGMG8d0oWu7SIxGsWjqTImkKwjCWWn1tkNU2d0YJIkxA46/0rdm8dMhWwFPDHmGyztedUyydXqdfLztA17dNI1ISyRWp5UqVxUGgxGHt/4lNwYMBJuCqfJUUeHWR70SEhelXsoLI19k3u7vuHLeRcjR3egW3Z2Mwk3c1vsOZo55n5iQaKKDQyl11E/gzaVDUjhP3TKQXfsrWLwhn/SdRVRUuVi99dBJnxcebOaa0Z0Y0TupQdP3wsmJpCsIwllH1TQW+xZQDeoeT3R4/XrDO0qzmbTuObYUZvLIoMe5vtvf611nC/pN5L/Z+SVT1k8kwBhAhaOcMkcpksGgX0dbZzBqwIDFFIjdY6PKU1X72LVdr+fRwU/y2Y6PGfvNufRPGESf2L5kFG7i333+j5kXzjrmfrotSZIkuraLpGu7SArL7azaUkBBqY2SCjvFFQ6sNjfBFhMd24TTOTmCjm3C6dImEkuAsaW77jcanHRlWU4AsoDbFEVZ2HRdEgRBOLmtOSW1U59jB7WrfTyvch9TN0xiSd6v/LffA7x74WwCTfUTsqZp/LL3Jyau/R82j50iWxFu1YXBYMCrekHz1rY1YCDAGIDD66i9obxJMvHPXrdzV9//8H7WO4z5eiQj24ymf8IgMgvTuavvPbwz9oNjrvFtbeIjg7j6nI71HnN7vBiNBnHNbRM6nZHuLEDU+BIEocXVjHK7to2gQ1J4gwpbAKw5uIrn1jzDgar9VDoqcHgdGCT9PrWqqta2M2DAZDDhUl21U8wWo4V70u7l2i43MHPLW4z5ehRjUsYyMGEw6wrW8H9p/+XdsbMJNbfc7fX+KLNJjGibWoOSrizLdwHVQH7TdkcQBOHkDhRXs22vvnhpeL9IJq97/pSFLbKKtzBx7QQ2F2bg8jqxuW0goSdb7UiyNUpGJCQ8mgeX77Z7IeZQHhn0OOe2O583M6Zz+bwLuaTDZQxIGMyKA8u5O+1e3rvoI0LM4v6xwqmdMunKstwFeAgYAqSf7gYkScLQSBWea07i+8PJfH+JxV/iABFLa3S8OH5P348XJ4Xhi7lr/TwuTL2I329YSbvwlGOen1O+hxfXvsCSvF8BqHJVHamJXOecrVHSR3jeOlPLkZYo/jf8OXrE9mL6ppd5K2M6V3S+in7xA/gt71fuHfAAH132KUGmht1Vx19+JyBi+SMkTTvx0nVZlk3AKmCCoig/yrK8F/jP6ZzT1TRNO92ybIIgCMdTXm3nghcfZbvxc/rE9Wf29dPpEdfjmHYF1gKeX/48c7LmYDFYKHeW49W89Ua1oCdbTdNqb0wAkBiayGsXvUZ8SDyTVk4iuzibv/X4G9uKtrG9aDvjR4zn9v63H3OuWBDqOGHSO9VI92kgU1GUH890yyUl1Y060o2MDKG8vBpVPburoPhLLP4SB4hYWqOaOErLrMzb+R1PLX0WlxTGUNd4Prr6dkKNZkpLj1yCU+Es5/VN05mV9S6BxiAcbgdW1VrvJgSgJ1uvptYb2bYLS+Gl0a+ABC+vfoliWzFXdLoSl9vDN9vmcv/Ah/jwos+wGC3YKj3YOL1Lf/zldwIillOJjj7xef1TJd3rgSRZlq/3/T8c+EKW5RcURZnckI1rmobXe+p2p0NVNb8pPeYvsfhLHCBiaU00TeOX3b/w2KLxaEBvxx2Ybd05N60NQQGm2tjsHjuzst7l9fSXsRgDcXgcWF3WY17PgBEVb71k2yWyK1PPmU6Jo4gX1j6HV/VyacfLWVewhu92f8f9/R/iOvlGAowBAH94f57tv5O6RCyn76RJV1GUegVJz2R6WRAE4UxsPLSeSesmUOQoZPzgp0hyD+PNb7cCcIGvGIZH9fD5jk+ZvO4FJEnC5rZR4aw4ZmRrwLdCmSPJtndMX14aPZ2d5Tt4ZPl9hAeEc3nHq1i+/3fm7vyKBwc+yjVdrsNsFHfQERqPKI4hCEKrUlPYIqtoM48OHs/dI+6kstzB5E/1dZzd20eR/P/s3Xd4VEXfxvHv2ZbeQ0ISSCAJbOi9dwHpoFQBC772LgiKqDyKooIiUlVsqEgREESa9F4CJKGzoQVCSe/ZzbZz3j8WEIRAgCSEMB8vr+eB7Dk7s7vm3jln5jf+riw7sYRxO8ditBnJNmdhk203Cdt/79k2rdicT1t/wZ7k3Ty75kmqeIUzJOoJ/klYxcL4eQxvNIq+1QZcV0xDEIrDbX2qDAZDlRJqhyAID7gbFbZwc3JBo9JwLiWPo2cyUVDwqZJAhwUvk2xMItecg00pWti2DWnPuFafsj5xHUNW9qdBhYY8V/cllp1cwrxjcxjR+G0eieyHWiXWqgolR3yVEwThnipKYYu1exPJVMVz3P0Xth4+h8lqvGHYSkgo/Dsb2VEXuRvvNvuAZSeX0m9ZL9pWas+bDUeyMH4e8479xluN36FneB8RtkKpEKErCMI9kWPOZmbc1FsWttibuJ8vDa+Q6nYIsKJYrh3Bwr9hezmEVajoE9mX1xuO4A/DPPos7UaPqr15u8kY5hz9FUOmgbcav0OP8F6opGJaXiEIRSA+bYIglCqTzcSM2Eof+8MAACAASURBVKk0n9uAC/kXWDdwK5+0nnBd4J7PPcdLa56j9ewWJKtjsWPGju2awJUuLYe8OmyHRj3JmgGb8XTy4tG/umOTrbzX7EPiUmOZc/RX3mr8DhsGbqNXRB8RuEKpEyNdQRBKxeWZxl/u+ZwGAY1Y0mclet+o6x6Xbkpn0t4J/H70F+yyHatsR8F+w3IDl8NWLal5uvaz9Ks2iJ8OzWLAst48UfNpPmg+jh8OfsuepN282+x9Ood1vW5rP0EoTSJ0BUEoUbIi8/fJpXwe/QlBbsH81PU3GgU2ue5xedY8ZsZOZWbcVGyyDVmRsSk2uMnSSY2k4cV6r/Jwla58d2AmT6waxLN1XqB5cEu+2z8DD50HY1uM46HQziJshTJBhK4gCCVCURQ2Jq5n/K6PUEkqPmvzJe0qdbgu/Cx2C7MP/8jE6PGYbWbsit0Rtlf7T17qVDreaPgWTYOaMzNuKn8eX8gL9V7modBOzIybip+zP5+0nnDD5xOEe0mEriAIxW5vUjTjd31EsjGJd5uNpWd47+vCzy7bWXz8Dz7c8T55llxssu36sP3PKNdZ7czIRqPR++mZHjeVhfHzeaX+G/QI78302K8Jdg9hYtvJtA5pK8JWKJNE6AqCUGyOph/hs+iPOZi6n5GNRzMoash1RSYURWFNwmrGbBtFSn4yNsV2TVnG60jgqnHlnabvE+QWxLTYr7GdsPJKgzcw2UxMi/2aMI8wvu4wg5YhrUu4h4Jwd0ToCoJw125U2OJGu/DsurCDUZuHczr7JHbFfvOwVUCtuPBUxEjqVw1i2r6v8dB58GbDkaQVpPL57k+I9KnG9I7f0TyoRQn2ThCKjwhdQRDuWFEKWwAcTjvEqM3D2Z8Sc8OiFv/lpvakau4QVBqFdWm/Em8J46NWn3ImJ4EPto+mhl9NZj38M40rNi2prglCiRChKwjCbStqYYuE7NO8u3UkmxM3YlPs3HQqMuDr7MeYpmOZt2U/h5wXEO5ei18emc3O09GM2PQa9SrU5+euc2gQ2KiEeiYIJUuEriAIRWaymfjp4PfMiPuaTmFdWDdwK5U9Qq97XLIxmbHb32XZ8SXYufXengEuAYxu9j4X8i4wbueHuFtr0dj8Ds0bmhjy5xAaBDRiTvcF1K1QvyS6JQilRoSuIAi3VNTCFjnmbD7Z9RG/HZmN/b8zka9yuWxjRbcg3m4yhhNZxxm3cyzdq/ail3YC++zbiPOYiF9eW1YNXUVlXUS52bdVeLCJ0BUEoVCXC1t8tvtjgt1DCi1sYbKZmLz3C2bETsGqWAs93+WwDXYP4a3G73AgNY5xOz+gf/VBLHvkH+YdXMKPeaPwV9fh6xZz6duoFb6+7mRk5JVkNwWh1IjQFYS7UGCxkZVnwS4rBPm6olKVj7Wh/y1s8XnbSTcsNGGTbcw68A2f7foYs1xQ6Pkub7VX2T2U1xuOIDp5Fx/vHMsTNZ9mdb9NLD2xiL7LehAiNaKF8ROq++jpVa9ZSXdTEEqdCF1BuA0X0/P5JzqR4+eyyMozYzL/e7/SxUlDZIgX1Sp5ERXmQ0Sw531ZoGFP0m7G7/qIFGNyoYUtFEVhgWEu724ZRb6t8FGoWlJjV+yEeobxUr1X2Xp+C5/v+Zhn67zI2gGbmX9sLt3/fIhOYV34rfPffDs3Bbus0KlxZVT34WsnCLciQlcQbkFRFI6fy2b17rPEnUgr9HEms42Dp9I5eCodgOqVvBjQIZKIEK/SaupdOZp+hM92j+Ng2gFGNXmXgfrB1xW2AFh9eiVvbHiJTHNmoefSSBpsio0wjyr8X53n2ZC4lskxX/Jy/dcY1+pT5hyZzcOL2tO1Sg9W9ltPuFcEizefxC4ruDlraFmrYkl2VRDuGRG6gnATOUYL3y87zOGEfwPG19OJtnWDCfB1wcfdCW8PJ+x2hRPns4lPzCI+MYu07ALiz2Uz/rd9NNJXoF+7CCr6ut7DnhTuTE4CE6M/ZWPiekdhi4dn37Cwxc7z23l+7dMkG5MKPdflsK3iFc7QGk/wT8Iqvj/4Da81GM5X7afx08Hv6fhHa3pG9OGf/psI86wCgNlqZ1PseQDa1Q/BSSc2lBfKJxG6glCIs8m5TFt8kPQcx73KygHudG0WSpOoADTq6/dhDfZ3o229YBRF4cDJdBZtOsn5tHz2GVKJO55G//YRPNykcpm55Hx1YYtn6rxw08IWw1YN4UxuQqHn0qq0WGUr4d4R9Ks2kBWn/2aBYS6vNxxBq+A2zDrwDR0WtKR3ZN8bLjPaeTiJ/AIbapXEQw1DirurglBmiNAVhBvYeyyFH1YcwWKV0WpUPNVVT4taFYsUmJIkUS/Snzrhfmw/dJGlW0+TmWtmwYYTnE3O5amuUei0924kd3Vhi4H6wWwfsg9/F//rHncmO4HHVw7EkHms0HPpVDossoVwrwi6h/dixallrDq9nBGN3qZBQENm7p/GmK2j6Fd9IBsGbifEo9J155AVhTXRiQA0jgrA1/P6UbYglBcidAXhKoqisGTLKZZuPQ2Aj4cTr/atQ9Wg60eAt6JSSbSpG0yTqAB+WnGUvYZUdh5O5kKakVf71sHPq3TDxWQz8ePBWcyMm0LnsK6FFrZINaYyeHk/DqTFFXquK2HrHclDoZ1ZfnIp0Rd38UnrCVT31jMjbgpvbnyZgfrBbHlsNxXdggo9V2x8GkkZRgC6NK189x0VhDJMhK4gXGXZ1n8DNyLEk1cfrYOXu9NdndNZp+GlR2qzYucZlmw5xZnkXMb9soc3+tcjPPj2w/x2FbWwRa45hyErBrA7aWeh57o6bFsHt+XvU0s5nnmMmZ1+IMQ9hKmxX/H88WEMjnqCrYP3EOgaeNO2KYrCqt1nAKgR5kOViiX/egjCvSRCVxAuiTGk8uOyQwDUi/Dj5UfroNVcf+/2TkiSRM+WVagc4M6svw+Ta7QyaUEcIx+rf0ej6KKQFZmlx/9k/M5xhLhXKrywhdXEU6sGs+nchkLPdTlsI7wjaRTYhFWnl5NqSmFuz0V46byYGjOZv08uYWjNp9g+eN8N6zDfSHxiFqcu5ADQvXnYnXVUEO4jInQFATh9MYdv/jqEokBYRQ9e6FOr2AL3avUi/RnzRGO+mBtDjtHKVwviGPlYA8IqehTbcyiKwoYz6/l04TgUWWJC269oV7nDdY+z2q08t2YYK0//Xei5tCodNtlKhHcktf3rsu7MP9gVO38/ugaNSsOUmEmsPPU3T9V6hh1DYvBz8buttq7cdRaA0EB3albxub2OCsJ9SISu8MBLzy5g6qIDWKwy/l7ODB9YD2ddyf2nEeLvxsjBDZg4N5Y8k5Uv58cyanADQgPvPnivLmzxeefPaB/4MLJ87WOsdiuvb3iJxcf/KPQ8WpUOu2wj0juSCO9qbDu/mZYhrVk/cBsWu5mvYyaxJmEVw2o/y66hsfg4+952WxNT8q6sae7ePKzMzOoWhJJU/F/lBeE+YrHambJoP9n5Fpx1asY+2xwfj7u7h1sUlSq4M/Kx+rg5a8gvsPHl/DjOp955feGj6Ud4cuVjPL/maceM5KHR9KvZ75ogs9qtjNj4GiHf+RUauFqVFhUqIrwj6RjamaT8i1T1Cmfb4L08U/sFPtv9MT3+7EyoRxi7h8Yxuun7dxS4wJV7uRW8nWmkL9rlaEG43xUpdPV6/UC9Xn9Ur9fn6fX6w3q9/pGSbpgglIY/t5ziXGo+kgQvP1qbqsGlVz0qNNCDkY81wNVJQ57JytcL95OdZ76tc5zJSeCVdc/Tb1kvWoa0ZueQGIbUeOKaSlIWu4UxW0YR8p0/c47+csPzaCQNGklDuFcELUPakGZKoWHFxuweGsdA/WDGbh9N76VdiPSuxu6hcYxsMhovJ+877ntalonoIykAdG0ailolvv8LD4ZbftL1en114GfgGYPB4A68ASzQ6/XXL+wThPtIfGIWa/c41of2aBFGvcjS/0iHVfRg+KB66DQq0nPMTFl0ALP11vvPphhTeHfrSB5e2I4wzyrsHhrLi/VevaaSlNlmZuy296j0nT8/HPqOG20gr74StpHUr9CAbEs2ncO6EP34AbpV7cmozcN59K8e1PSrQ/TQ/QxvPApPp7v/YvLPnkRkRcHTVUurOoUvJxKE8uaWoWswGOKBQIPBsEOv17sDQUAuYCnpxglCSTFb7Py08igKUKmCG71aVr1nbYkI9uLZnjWRgISkXL7/+wiycuO9Y3PM2Xy2exxt5jVBI2nYPmQfbzcdc00lqQJbAR/v+BCX8S7MiJ16w/OoUaNV6ajqGU6UX00K5AIG1RjKnscP0LpSW15b/yIDlvWhfkBDoh/fz+sNh+OuK57JXpm5ZjbHXQCgY+PK97RQiCCUtiLNFjEYDHl6vb4qcAKQgJcMBkNOibZMEErQos0nSck0oVZJPNOjZonMVL4djaMCGNAhkj82niAmPpVFG08y8KHIKz8vSmELk83E1H2T+GrfFyg3GNWCYz9brUpLZY9QVJIKlaTipXqv8mi1/hxOO8hza4YRm7yPVxq8zoyOs3DVFn+96OU7E7DZZdycNXRqdH2FKkEoz25nimYi4Ay0AZbp9frjBoOh8IV9l0iSRHHdrrm8V2l52LO0vPTlfuzH0TOZrN93DoBeraoQHuIYJd7rvnRvEUpqlomNsedZHX2Win6utK4XwNyjv/FF9AQaVWzMX31XEfWfwhb51nxmxExlYvRnNw1bnVpHsHsIdtmOu5MHIxqPpHt4T2KTYxi2ejAHUg/weqPh/ND1Z1w0LiXSx7RsE1sujXK7twjD3VV708ff6/ekOIm+lE2l3RdJKeQy1s3o9fpfgGyDwfD6rR6rKIoilgIIZUWB2cYrX24kJcNI1WBPJr3R7p6Pcq9mt8uM+3E3+wxJJOt2kFrhTyL8q/BZx89oGtL0msfmWfKYtGMSH2/+GDuF3wd2VjsT7BGMyWaiul91xrQZQ+fwzuw6t4txW8ZxOOUwo1uP5v8a/N8NdxcqTtMXxvHPrjN4uev4fkxnXJzEqkWhXCo09G75idfr9d2BEQaDodNVf60DsoryzOnp+cU60vX2diMrKx9Zvv0vC2VJeenL/daPJVtOkZJhRK2S+L/uUeTmGK/8rCz0RVEUIuudY8bFMdjs0CjrGb7r+zy+Ls5kZDiWFOVYcvg2dgZfRk+4adi6qF3wd61AvjWfCK9IhjceSbPgFuy6sIMOP3fkVNZJ3mz8Fj89PAcntRPGHBtG7nzZ0q2kZJpYF+0ohtG9eRim/AJM+Tc/piy8J8VF9KVsKom++Pq6F/qzonzNjAEa6/X6J4Dfga5Ad6BZUZ5cURTst56MeVtkWcFuv7/f6MvKS1/uh35k5ppZudOxNrRjo0qE+LvfsM33qi+XC1ukGlN4t+U77NwQiNkiM3XRQUYPbYDRnst3+2cyee8XtxzZ+rr4kW/No2FgI15vMII6Feqx/fxW+vzZg7O5ZxnecCQD9I+hU+sASqW/S7ecwi4reLnraFcv+Lae8374fBWV6EvZVFp9uWXoGgyGJL1e3wuYDMwA4oFHDAZD4ft9CUIZ9Ofmk1hsjgk8vVpVudfNueJo+hE+2z2Og2kHGNXkXQbqB6NRaajjmsq0Pw9iuHiBx+f9xubcX5CRCzmLhIvaGQ+dJ0ZbPu0qt2fsQ+9TQQph09lN9FnajaT8iwxvNIp+1QaiVd/8Xmpxu5iez47DSQD0bFFFzFgWHlhFnb28FWhcwm0RhBKTkJTD9kOOX/p9WlfFzbl0Q+dGzuQkMDH6UzYmruf1hsOZ9fDsa+6phoWqsFb9izWpP0MOhd4lclG74q51w2g30jOiN680eIMwr1D2Zu7gqQ3DyDBlMLzRKB6t1v+aohml6a9tp1EUx1aJbeuJdbnCg0vMYhDKPUVRmL/+BAAVfV1p3yDknrYnxZjC5H0T+TN+Ic/UeYHdQ2OvWWebZkrj671f8v3BbxyzkVU46looXBO8LhpXnNXOWGULA6OG8GL9VwlwCWD92TU8v2YYRns+wxuNolfVR1Gr7t3I8sS5bKKPOqpP9WpVBa1GjHKFB5cIXaHci4lPJT7RMe9v4EORaNT3ZrZyjjmbGXFTmH3oR0d95CH78Hf5twpWijGFL/d8zi+Hf7x+6Y/EleB10bjipNYhKzLP1nmBZ+u+gLeTD/8krGLS3glY7GZGNR3NU02HkpVpvKf33GRZ4fd18YCjCEmbumKUKzzYROgK5ZrNLrNw40nAsUl6vYjb23quONyqsEVS/kU+3TWOBYa5ha6zBVArTiioUOxqXm08gv+r+yyuGldWnV7BpL0TUBSFtxq/Q/fwnmg1alTSvV8Kte3gRc4k5QIwpFN1UWNZeOCJ0BXKta37L5CSZUICHutYrVS3j7Parcw7NodJeyfQMLAxS/usorqv/srPL+Sd53/bx7Ds5NKbhq2LxhVJkdBpXaiU04/K1o64JlVmg9davtr3BRqVhlFN3qVrle5lans8Y4GVRZscX3iaRAUQFSb2yxUEEbpCuWW1yazY5Vgi1LxWIJUDCl87V5xkRWbZiSV8Hv0JIR6V+bnrHBoG/jsPMTHnLO9uGcmas6tveh4XtQuKouDr7Mvopu/Tt9oA/t6ewKzoeXx2aiQBaV6MazeWTmFdylTYXrZ062nyTFZ0GhUDO0Te+gBBeACI0BXKrW0HL5KRY0aSoGfLKiX+fIqisDFxHeN3jUMtqZjQ9ivaVe5w5eensk4ycvMbbDu/5abncVI5oSgKgW5BfND8I3pE9EJWZJaeWMzkc19g9NRSI3sYgcaGhFC/TAbuudQ8NsScBxzlHv28SrbSlSDcL0ToCuWSzS6zcmcCAM1qBBLk51aiz3d1YYvRzT6gZ3jvK2F4LOMoIza+yt7kPdcdJyFdubSsU+mQZZkqXlX5sOV4HgrthF2xs9Awn8n7vqCCawCftvmCxv6t+XTOPi6mG5m55BDvPdmoxPt3O2RFYe7aeGRFwd/Lma5NQ299kCA8IEToCuXStoMXSc8xI0GJFsIorLAFQGzKPoZveJUjGYevO06FChkZBQWtpMOu2InyrcHHrT6nRUirK/eDv973JSHulfiy/RRaBbe5EuRv9K/LJ7/uI89kZeqiA7z3ZGPcXe792mOAtXsSOXbWMVv8sY7VRCEMQbiKCF2h3LHZZVbsSACgac2SGeXerLDFtnNbGLnpTU7lnLjuOLWkxq7YkZHRSBrsip16AfX5rM0X1AtogMVu4bcjs5mybxJhXlWZ8tBMWgS3uu48AT6uvNq3Dl/MiyU508TMJQcZMaj+PVsOddnZ5FwWb3ZMnmpRK5CG1Svc0/YIQlkjQlcod7ZfPcot5nu5Nytsser0CsZsGcX5/HPXHaeVtFgVK3bFjlpSIysyzYJa8HmbSej9ojDbzfx86AemxUymmk91ZnT6nmZBzW/aluqVvXmqaxQ/rTzKsbNZ/PqPgae7Rd2ze7wWq51Zfx/BZlfw83RmaGf9rQ8ShAeMCF2hXLHZZVZc2tSgSY0Agv2LZ5R7s8IW84/N5eMdH5BakHrdcTpJh0WxYFWsqFChoNC2UnsmtP2KKl5VKbAV8OPB75gW8zU1/WrxfZfZNApsUuR2ta4bxMX0fFbtPsu2AxdxddIw6KFIbrKzWIlZuOkkF9LykSR4rldNXJ3FrxdB+C/xX4VQruw6nExadsGle7lV7/p8hRW2kBWZ7/bP4Is9n5Njyb7uOGeVMwVyARbFgnQpADtX6crEtl8R5B6M0Wrku/0zmBE3lfoVGjC72+/UD2h4R23s1z6C7HwLOw4lsWZPIq5OGh5tF35X/b5dB06ms36fY4Tfo0UVqlf2LtXnF4T7hQhdodxQFIV/Lu3X2rB6BULuYpRbWGELi93ChOjxfBM7DaPdeN1xLioXTLKJArngStj2DO/DxHZf4efiT741n5lx05gZN5XGgU35vfsf1KlQ747bCaCSJJ7uHkWBxU5MfCpLt53GxVnDkG417+q8RXUxPZ8flh8BoGqQJ73L0A5OglDWiNAVyo2Dp9I5n+bYFb1r8ztbpiIrMkviFzN+1zgqeYReKWyRZ81jzNa3+fXwT1hky3XHuapdMdqNmGQT4FgK1LfaACa0nYSnkxd51jymxkzm2/3TaRncmgU9l1DLv/add/Y/1CoVL/SuxdTFBzh8OoN5647j4+1KM73/rQ++Cxk5BUxaEEeeyYqrk4bne9e855O5BKEsE6ErlBurdztGudUreRER7HVbxyqKwvoz6/hs4ccossTEtpNpV7kDqcZUXl3/Aovj/8CuXL9xvKvKFaNsvDLqlZB4LOpxPm09ETedG7mWHL7e9yWzDsykTUg7/uyznCjfGnff2RvQalS8+mgdJv0Rx4lz2cxctJ/zravQu1XVEplclWO0MGlBHBk5ZnQaFW8OqEegj2uxP48glCcidIVy4fTFnCtrQ7s2C7utY6Mv7mb87g9JM6XyeefPaBfQmZMZJ3ly5WOsSVh9w43jL49sjbIjbFWoeKLmMD5u9TnOWmeyzVlM2juBHw58S4fQTvz1yGqq+VS/+47egpNOzZv96zH9zwMcO5vFX9sSSMk0MaxbDbSa4huBmsw2Jv+xn4vpRtQqiVf61iGy0u190RGEB5EIXaFcuDzKDfJzpW5k0XYS+m9hi8E1h5BoOUnvP7uz68KOQsLWDaM9/8rIVoWKp+s8x0ctxqPT6MgsyGBK7CR+PvQ9ncO6srzvGiK8qxVfR4vA1VnDyMENmLPuOJv2nWPn4WTSc8y82rdOsRTQyMoz883SQ5xJykXCMVO5Tnjp794kCPcjEbrCfS8ly8Reg2OT9C5NQ1Hd4lJqQvZpJu75lE2JG3ij4Qi+6/wzu5N20nF+O45mHL7hZWQXtSsmuxGj3XHPWELi+bovMbbFx2jVWjIK0vlu3wx+OfwT3ar2ZFW/DVT1Kt0ZxFfTalSMGNwQLxcNf21LID4xi49+jmZI5+o0qHbnBSsOnEznxxVHyDVaAXi8i56mNQKLq9mCUO6J0BXue2ujE1EU8HLT0aJWxUIfd3Vhi2frvsinrSeyKXEDbec343zeOWyK7bpjnNUuFNhNmK66Z/tC3VcY23IcGpWGNFMa38RNY86R2fSMeIR/+m8izLNKSXX1tkiSRN92Efh5uvDL6mOk55iZtvgg9SP9GdK5Gv5eLkU+l80us2jTSdbsSQTAWafmyS56mt/k9RYE4XoidIX7Wp7JytaDFwDo1LjSDe9bZpuzmBk39Uphi/UDt7M2YRUt5zYmy5x5w7B1Ujlhls0U2P+djfxCvVcY28IRtinGFGbGTWXu0V95JLIf6wduo5JH5ZLt7B1qXTeIqsGezPnHgCExi7gTaRxJyKBj40o0iQogLNCj0IlWWXlmdh1OZuuBC1xMd3zxqBrkwQu9axEgJk0Jwm0ToSvc1zbGnsdilXHSqmnfIOSan/23sMWSPitYnbCSdvObY7IZbxi2OpUOi2zBLJuv/N3zdV7mfy0dl5GT85OYHvs1Cwxz6V99EJsG7STYPeS685Q1If5uvD2kATsOJfHHxhPkGq2s2nWWVbvO4uvpRINqFagc4I5dVpBlBatN5siZDA6fzkBR/j1Pt2ahPNo2XCwLEoQ7JEJXuG/Z7DIbYxxVkFrXDcLN2TFJ6L+FLb7r9DNrzqym2+JOWGXLDcNWI2mwKbZr1uA+XftZPmk1Aa1ay4W880yP/ZpF8QsYpB/C1seiCXS7vy6tSpJEqzpB1Iv0Z9WuM0QfTSE9p4CMHPOValI34uKkpklUAG3rhRAe7FmKLRaE8keErnDf2nsshaw8CxLQqVElZEXmrxN/8nn0J1TyCOXDlp+w/sxaHl85EKtsvWHYqlAjY7/mZ0NrPMnnbSbhpHHiXG4iU2O+YumJxQyp8SRbB+8h0PX+njjk7qJlQIdI+rePIDElj5j4VOJOpJFrtKJWSahUEmqVRAVvF1rUqkiDav5iez5BKCYidIX7kqIorN3rmNRTJ9yXw3nb+WTdR2gkNU/Xeo6t5zczYtPrmG0FNwzbyyUaZf6dqdy/2gB+G/grxhwbpzMTmBLzFctPLuXxmsPYPngfFVzL1zZ1kiQRGuhBaKAHj7S5dzOtBeFBIkJXuC+dvJDD6Yu5ZKiPsUL+kz+2ZtItvCc7L2xn0t4J5FlysXP90h9wBK7Cvzcqu1XtyfSO3+Ht4sn5nPP8b/1HrDy5nGG1n2HHkBj8XMQaVEEQiocIXeG+9PvOTexxmUqeNoHeAV3YmxTN/GO/k2FKLzRsVaiQka8EbvtKDzGj0ywquAZwKusE720bxdoz//B/tZ9j19BYfJx9S7NLgiA8AEToCveVhOzTfLLjY1YlrcGXKHRa2Jy4kaT8izesIAX/hu3lnzet2JxvOv1AZc9QjmfG878d77Hx7Dqeq/ciJ14/gWzUYLcrNzyXIAjC3ShS6Or1+tbAJCAKSAMmGgyG70qyYYJwtWRjMpP3TmRx/B/4a8JRsJOnPoPRmkam9cYB+d+wre1Xl+mdvqWmX22OZRzlhTVPs/X8Zp6v+zIT2k7C28ULb2d3Mox5pdk1QRAeILdcbKfX632AZcBUwAcYAHym1+s7lXDbBIFscxaf7hpHq7mN2HVxB3bZTnJeEjYpn3xV8jX3Zi9TXfpYXw7bqp7h/P3IP2wYtA1FgWf/eYq+f/Wkln9doofu581GI/HQiaUwgiCUvKKMdMOAFQaD4fdLf47R6/UbgZbAuhJrmfBAM1qN/HhoFtNivsJT5wUKmKwF5NnyQLrxSPS/I9sAl0C+bP81Xap051D6QYatGsqepN28XP91pjw0EzftnW9yLwiCcCduGboGgyEOeOLyny+NfNsAvxblCSRJQlVMxWtUKuma/72flZe+FHc/rHYrvx/5lfG7xqGSVKglNVqVlhxrDjnWnH8fKF39fx2zkWVkJCQ8tZ580vYzHqsxlP0pcTy149kvvgAAIABJREFUejCxKTG83vBNvuvyA67aG5cvLC/vCZSfvpSXfoDoS1lV2n2RFKXoE0b0er0XsALIBXoYDIYbz1y5iqIoSklsoC2UL7IiM+/gPN5a8xZGqxEvJy+ctc6cyDhx7QMvf1yla5f+SEi4aFwY12EcrzV7jdiLsYzbMo79Sft5p9U7PNvwWVy0RS/wLwiCcBcKDb0ih65er68KLAdOAoMMBoOpKMelpeUpxTnS9fZ2IysrH1m+v2eXlpe+3G0/FEVh1anlvLN5JGmmNEI8KqEoCgk5pws5gGs+zipUaFVaXmrwKm82fouj6Yf5InoChoxjvNn4LYbUeBxnjXOp9KUsKS99KS/9ANGXsqok+uLr615o6BZ19nJDYDUwBxhZlBHuZYqiYL/xssk7JstKuVnSUV76cif9WH9mLW9vGc6FvPNEeEeikjSczj5V+AFXnV5ChU6lZWDUYN5p+j6nsk7wxIohJGSf4o2Gb/Frt/no1DqA225XeXlPoPz0pbz0A0RfyqrS6sstQ1ev1wfiCNxJBoNhQom3SCj3NiVuYNTmNzmbcxa9TxQVXAKIzzQU8WgJV7ULHcM6M6b5/7iYf4EX1jzNubxEhjcaxYDqj6FVa0u0/YIgCHeqKCPdZ4AKwAd6vf6Dq/5+isFgeK9kmiWUR+vPrGX01rc4m3MGvU8N/Jx9OZZ5pGgHK6BW3Ihwr8n0bl+Qbclm+MZXSTYmMbzRKPpVGyjCVhCEMq8os5c/BT4thbYI5ZCiKKxKWMEH20aTmOsY2XroPAsN2//WRVahwkPjg2L2oIZ5GM92imLMtrfJMmcyovHbPBLZD41KFFYTBOH+IH5bCSVCVmSWHF/EuJ1jScq/SLhnBG4aNwyZx6485r8BC1wzG7miaxBatZZqxqFkm+Gc1x98GSszovHb9I54FLVKbDcnCML9RYSuUKwsdgtzj/7GxD2fkmnKoJJHZbQqHSdz/l36o0KFcumf/wavhESoexj59nxeazgcu8mdL6O/QHay83bd0TzXdDAqqZimwwuCIJQyEbpCscix5PDT/h+YGvMVRquJCq4VkCSJM7kJVx5zOWwvF7EArgpciQjPCNIKUhkYNZiq3hHMiJ1CenYBkeaBNPF5iOebNkOs+RYE4X4mQle4KynGFL6IGc/06OnIioyrxg07uVzIP3/lMWo0yNgLCVuo7q0nxZRMh9CO1PSvzfcHvkWn1vFS7ZGsXu4JikTnJqEicAVBuO+J0BXuyKnsk8yMncri4wtx0uhQSWryrUaMNuOVx2glLTbFhh3bDcM2yrsGaeY0avnX4YnAp5lzZDYxKXv5oMWHdAx9mIWbToJyFncXLc1rBpZ6HwVBEIqbCF3htsSlxDAt9ms2J27EReOCrMhkmjIvhakjWHUqHTbZhlWx3jBsa/jUJNeaS6B7RR6p3o9F8QtIzD3LR60+pUPljkiShNliZ0vcBQDaNwhGqxGTpgRBuP+J0BVuSVEUNiVuYHrs1xgyj+GqcaXAZiLHkg1wJVid1E5Y7RYssuXfY68J21oggU6lpU9YX1ae/htzopnP206iTUi7ay4f7zychNFsQ62S6NCgUin1VBAEoWSJ0BUKZZNtLDu5hOmxUzBa83FSO5FuSidFSYGrZh67aFwosBVgthfc8DxRPjXxdvIi2ZhM20rt2XRuA/tTY/mq/TRahbS57vGKorBu3zkAGkcF4OPhVJLdFARBKDUidIXrGK1G5h2bwzf7p+Pn5IdWpSUh+/SVfWodYYsjbO0FV+7j/vdScnVvPVW9wolNiaGmXy3O5Z3jdM5ppj30Lc2DWxb6/EfOZHIhLR+ATo3FKFcQhPJDhK5wRUZBOj8f+oEfD86inn99KrlVYufF7VdC9PIm8W5aN4y2fydNqXCsm70cyhFe1WgQ2JD1Z9ZQxSscjUpNliWTbzv/RNOgZrdsx7o9iQCEB3sSEexVEl0VBEG4J0To3gWrTSYly4RWLaHTqnG69O/9trHzudxEvt0/nT8M8+gY+jC1/eqyIXFdoWGbZ80DHEuBkBTsimMbqSoeVelQuSNLTiziQt55dGonFGR+6jqHhoGNi9SW5EwjB06mA2KUKwhC+SNC9zYZC6wcOJlO7PE0Dp5Kp8By7b6FapVEnXA/WtauSL1If7Sasls96Uj6YWbETmHdmX/oV20QTQKb8efxhVeFrRoZOx46D/KseeRacwHQSToUScEqW0GByh6VebRaf+YemUNM6j40ai2eTl7M6b6AegENbqtN6/aeQwG83XU01gcUd5cFQRDuKRG6RWQssLJgwwl2HErCfpONju2yQtyJNOJOpOHmrKFJjUC6NwvF39ulFFtbOEVR2HVxB9NiJnMgbT9P1BhG06AW/Hjouythq5bU2BU7njoPcq25ZF+apeysckGRFMeEKQUCXQJ5uu5zzDfMYdWpFcjIVPKozFcdplHHv+5tty3PZGXbgYsAPNSwEhp12f3CIgiCcCdE6BbBgZPp/LL6GJm5ZsAxmo0K86FBNX9qVvFFksBssWOxySRnGNl5OImjCZnkF9jYFHuenYeS6N8+gg4NQ1Ddo6pKsiKz+vRKpsVOJqMgnSdrPI1KUjNp379bJGskDTbFhqfOixxLNlmWLADcNe4oKOTbHJOb/Jz8eaXBayyKX8ivh3/GZDPSrlIH3mw0ipp+te64jZvjzmO22tFpVbRvEHJ3HRYEQSiDROjehLHAyvz1J9h20DH60mpUPNKmKu3qheDqfOOXLjLEi1Z1gsjIKWDn4STW7Ekk12jl97Xx7D2WwrDuUQT6uJZaH8x2M4sMC5gRNwV3rTtDazzJqtMr+GjXv1sjXwlbJy+yzJlkmjMA8NR5IiFdGel6ab0Z2eQdVp5ezvS4KVhlG53DHmZcpw8J0oRhtxd+BeBWrDaZdXsdy4Ta1A3G3UXsjSsIQvkjQrcQ2XlmJs6L5WK6Y4ZuRLAn/9ejBkF+bkU63tfTmR4tqtCmXjBz18YTfTQFQ2IW//sxmie66GlbP7gkm0+uJYdfDv/MrAMzqeFbk9cbjuCPY3N5e8uIK5eRL4etl5M3meYMMgocE5i8dd6oVWrSL/3ZTePGmGZj2XZ+CxP2jEdBoVvVngxvNIoofz2+vu5kZOTdVXt3HUkiO9+CJEHnJpXvrvOCIAhllAjdG8gxWvhifhwX042oVRJ924XTpUnoHc1K9nTV8WKf2jStkcpv/xjIzrfw44qjZOdbeLLnnV+KLUyyMZnv93/DnKOzaV/5If7X8hN+PPAtb2x4+bqw9Xb2IaMgnfSCNAB8nHzQqZ1INiYB4KRy5r0W/+No2mE+3vU/JEmiR3hvRjZ+h3DvyGJrs6IorIl2LBNqVL0CAWXk/rcgCEJxE6H7H3kmK1/Oi+NCWj4qSeLFPrVoVAyzaBtWr0D1yt5MX3yA+HPZLNp0kgKrTL+2VYuh1XAq6wQz4qbx98klPBrZn09bf8G02MksOb743wlSqJGR8XH2Jd2URpopFQAfJ1/ctG6cy3MEn1bSMqbZWJKNF/l010coKPSK6MPbTd6jilfxtPdqh05ncP5SMYwuzUKL/fyCIAhlhQjdq+QXWPlyfiznUvOQJHi+d81iCdzL3F20jBhUn1l/HyEmPpXl20+TnJHPsz1q3HFB/9jkfUyL/ZqdF7bxZK3/Y3zriXy5ZwKzD/+EcqlYxeWw9XPxJ9WUSqopBQAfnS/ezt6czjlFpjkDNWpGNh0NMkzc+yl22U6viD6822wsoZ5hxfY6/Nfq3WcBqFbJSxTDEAShXBOhe4nNLjNl4QHOJuchAc/2rEnTGsW/nZxOq+blR2rz+7p4NsacZ8/RFArMdl7rV6fIS2QURWFj4jqmxXzNmZwEnq/7Eh1CO/Llns9Jzk+6Uhnq8qbx/q4VSDEmk2JKBsBH54O/awDHswxkWjKQkHitwXAquAYwMfpTTHYTPcN78b8WnxDiUbIFKs4k5XL0TCYAXZuKUa4gCOWbCN1L/tx8ihPnHbN0n+5egxa1KpbYc6lUEk911RNUwYO5/xzj4Kl0flxxlOd61bzpkiKbbOOvE38yPXYKsmLn+XovY7TkM2nvBLLMWdeELUAF1wBSjMlX7tF66bwIdq/E0YzDZFocQfdMrReoE1CXcTvHkm3OolvVHoxvPZEg95Kd6HXZqt1nAAj0caFeNf9SeU5BEIR7RYQujnW4q6MdlzgfblKZ1nWDSvw5JUli8MN6cnML+HtHAruPJOPurGVI52rXbHEHlzcg+I1v4qYT4lGJEY1GcTzrOB9sG43RarwubANcA0i+Kmw9tV6EeVbhUPoBsjMOA/CYfigdQx9m7I7R/HzkezqHduGLdl9T0b3k+37ZxfR89hx1XOru2iz0nq1hFgRBKC0PfOhm5pr5YfkRAKpU9KB/+4hSff5+7cPJMVrYHHeB9THn8HDV0ru1Y7JSRkE6Px6cxc+HvqdJxeZ80W4ymxI38sr6F7DYzdeErYREBbcAkvOTSDImISHhrvEg0ieS/alxHEzfD0DP8D4M0g/m/W2jWWCYS/vKD7G638ZSG9lebfmOMyiAr6cTreqUXtgLgiDcKw906Mqywvd/HybPZMVZp+bFPrVKvfSgJEk88bCefJOVvYZUlm47TYE6hf22xSyMn0/3qr34scsc/jDM5fGVj2FXbMjKv1vsqVBRwTWAJONFkvIvokKFi8YVvU8UcamxxKXGAtChcieer/MiY3eM4clVg2kR3Io/+yynsue9uY+akmlk9xHHPebuzcNEyUdBEB4ID/RvuuU7Ezh21lHqcFi3KAJKsVLU1VQqied61cK/UgaxzpMZHtOXnDyFuT0WkWPJof+yXsw/9jtW2YKsyEhIqCUNga4VsWMnyXgRNWpc1a7UD2hAgd1EbOo+FGSaVWzOvB6LSDEmMWTlADydvNg5JIalj6y8Z4ELsGLnGWRFwctdR5tSuJwvCIJQFjywoXsuNY9l2xIAaFsvqERmKheFoijsOL+NJ1cPYIX1XUJcImmSP4aNJ3bRe0lXVieswCpbsSt2JCQ0koYA10Dsio0k40U0kgYXtQt1K9SnQDYTk7IPWZGp7VeHOd3+oMBuZsiKAUio2DRwB6v6rSfcu3Qvof9XWraJHYcc95u7NQu74+VSgiAI95sHMnQVRWHOmnhkRcHfy5nBnaqXehtkRWbJ0SV0WfgQIza9RvfwXszq/BNGrxh2ur1PmuoINsWGTbZdCdsKLgHYFBvJxiQ0khZntTO1/etikS3Epu5DVuyEe0Xy08O/4axx4clVj5FvzWN537VsGLSNGv7FXwHrTqzcdRa7rODpqqVdCZfDFARBKEtu656uXq9vCiw1GAz39W/KXUeSiU90XFYe0qk6TtrSG2mZ7WYWGuYzI24Kvq4+vNLgDZwkZz7a+T6nck6hU2lRJDuKYgcFJEmNv7MvqQWppJiS0aq0aCQN1Xz0HEk/RFxqDADBbiG81+xDfjv6M8+tHUaQWzDzei6mQ2jHUutbUWTmmtl24ALgqD5Vmq+9IAjCvVak0NXr9RLwNPAVYCvRFpUwY4GNPzacAKBehB/1S2ltaI45m1+O/Mz3B76hpl8tvmg/mQJVLqPWvkNyfhKuGhdsshWbbAVALWlQy25YyCa1IBUnlRNqlZqqXhEYMo9xIC0OAD9nf0Y3/YClJxfx5qaX8XLyZmanH3gksu91S4/KgpU7z2CzK7i7aOkgtu8TBOEBU9SR7hhgIDAeeKfkmlPy/tp2mux8Cxq1isGdS/6ycnJ+ErMOfMOcI7PpENqJX7vNJzZlH8//8zRZ5iw8dZ7YZCs5FkfYaiUtHk6eZBSkY1dlo1K0IKsJdA3lYsFpDqcfBMBD58nIRm+z7uxa3t/+Nk5qZ8a3nsgTNYehVpXN0WNyhpFNcecB6NK0Ms66B3ryvCAID6Ci/tb7CfgUaHe7TyBJEqpiunN8eZefO9ntB+Bsci7r9zn2bO3ZMowgv5KbrXwi8zjTY6aw7ORfDNAPYmX/taw4uZz+y3phtBrxdfbDJtvIKHDsXauVtLjr3Mk0Z5JRkI6LxgWtpENj9ybLfp6z+fEggYvGlVcavM6ei7v4fM94VJKKkU3e4aUGr+KiKf3deW7nPVm85SR2WcHHw4kuzUJRq8vWSPxuP19lSXnpS3npB4i+lFWl3Zciha7BYLgIoNfrb/sJ/Pzciv0yp7d30fa0vZqiKEycF4esKFT0c+XxHrVK5H5i9PloJmyfwNYzW3m5ycvs67iXWftm8dCCNthkGwFuAeRacq/UQdaqtLjp3MgqyCLTnImrxhVnjTN+rn6czT5LjnwGJFApGvT0okJQJt/tn4FdsfNKk1d4r+17eDt7F3s/btet3pOjpzPYe8yxq9GT3WsQFFh2Nza4k89XWVVe+lJe+gGiL2VVafWlxK/vpafnF+tI19vbjaysfGRZua1jY+JTOXzKsSn74I7VyM81kV88zUJRFNafWcu0mK9JyEng5Qav8X7Tj5i8ZxI1Z9REQaGiaxCJeWc5n+u4vKqVtLhqXcm2ZJNdkI2rxhU3jTuuWleSjBfJyHCMgNWShh6h/dlx6jDHVWs4kSjTP6ovY1qMJdg9GNkIGca720D+bhTlPVEUhVlLDgBQKcCd+uG+d73pfUm4m89XWVNe+lJe+gGiL2VVSfTF19e90J+VeOgqioLdXrznlGUFu73oL46sKCzedBKAGmE+1An3u63jC2OTbSw9sZjpsVNQFIXXGr5Jo4AmjN/9IWO3vYdaUhHkFsyZ3AQS8xy1nTWSBie1E/m2fHIsObhqXPHUeaGSVGQUpJNa4KhFrJLU9KjakzRTGtuS12JxsuFnqkWU+Qla0pJAl6Bi6UNxudl7svdYypXNJAa2j0BRKFNt/6/b/XyVZeWlL+WlHyD6UlaVVl8eiJks0UeTOZfqGNf2bRt+1+fLt+Yz7+hvfLN/OpU9Qvmg+YdUcg/lgx2jeX39SzhpnAh1D+VUzknO5CYAjrDVqnWYbEZkm4ybxg1/N38KrGayLFmYbQUoKEhItKvcAaPVyO6kXagkFZHe1fhfy4+JP+jD+n3n+Cc6kdBAjxLdCam42OwyizY7vvDUquJD7XC/e9wiQRCEe6fch67NLrN062kA6kf6ExFy5/cS003p/HjwO2Yf/oGmFVsw6+GfUaFizNa32Z8ai4fOgyqeVTmRfZxTVkfQaCQNapUas92MbFdw07pTwSWAPEsOqfmpmGymK2HbpGIz7LKd+AwDzhpnfJ18+aDFR3QK64IkSTSoIHMuJQ9DYhazVx0jyM+VKhU9i+V1KikbY8+TkmlCAgZ0iLzXzREEQbinbit0DQbDJuC+2vR0+8GLpGSaAHikTdU7OsfZnDN8u386i+IX0DO8D3/1Wc2F/PO8ueEVTmSdoIKLP1W9wjmeFU+m2bFPrVpSo5bUWGQLyOCmdSfYNZjUglSSjUmYbQWXdgmSqOlbG5WkItmYjLfOCwmJ4Y1G0b/6oGuW/2jUKl56tDYfz95Deo6Z6X8eZOxTTfB0093161QSMnIKWLr1FAAta1ckNNDjHrdIEATh3irXZSCtNjvLticA0LRGwG3/0j+cdogX1z5D54Vtcda4sHnQLtpXfojHVvTlseV9MdvNhHuFk2RM4nhWPABq1GgkLXbFjoKCm9aNSO/qqFBxPv8cOeZsxyVmZCJ9IqnhUwOzvQBPJ0/yLbn0qz6InUNjGBQ15IbrbT1ddbzaty46jYqMHDMzlxzEZpfv+rUqboqi8Ns/BkxmO27OGvqLUa4gCEL5Dt2NsRfIzDWjkiQeaVO0e7mKorD9/FYeW+4I1pp+tdk5JIaqXuF0XNiGF9Y+g7vWnXDPSBJyTnM8K/7KFntqSY0dO2pJhbvWHb1PFBISZ3MTyLflYbwUthVdg6nmXQ0njRNVvKuQbkqjacXm7B4ax0v1X8VZ43zTNoZV9GBY9ygA4s9lM3fdcRSlbE1m2H00mf0nHbPFH+tYDa8yOhoXBEEoTeX2nq7ZYmfFzgQAWtWpSEXfmxfCsMt2Vp1ewfTYyWRbsnml/hvMeng2vxz6iaa/1yffmk/9Cg3w1nlzNMOx6b2EClCQJAlZkXFWueCsUhPpVY3jWQZOZZ/EbDNjxzF929fJDw+dJ+46d2r512L92bU0CWzGlsG7qeh2e9vbNa9ZkcSUPFbtOsum2PMEeLvQtdm926rvajlGC3PXHgegdrgvLWuX/QlfgiAIpaHchu6W/RfINVpRqyR6tyr8Xq7ZbuYPwzxmxk3FS+fFqw2G07ZSO6bETKbO7GpYZSstglpxIe88+1L2OEa1khpFkZEAGQUXtSuSBHrvKI5mHOV4VjwFdvOlzeYVPLQeeDp54e9SgcaBTVh5ajkmm4nt/7edCqqQO56m3q9tBEnpRmKPp/HHxhP4eTnTJCrgzl6wYjRv3XHyTFacdGqe7KIvkzWgBUEQ7oVyeXnZZpdZHe1YF9uidkX8vK6/XJtjzmZqzGQa/1aHlaf+ZlK7qfzeYxGbEtdT8+cIvts/nbYh7ansFsrW85s5mX0SjaRBQUG+6n6tm9admn61UBSFY5nHsMhmTDYTsmLHWe1EoGtFIr2rM0g/hHxLHscyjvJTt9+Y3X0Oev/br/B1NZVK4vnetaga5JjB/P3fRzh+Luuuznm34o6nsfuIo9pW/3YR+HuVfmlKQRCEsqpchu7Ow0lk5pqRgG7/ueSalH+Rj3Z8QJM5dTmafpj5Pf/kq/bT+PnQD9T5pRoL4+fTPbwXFd2C+efMKhJyT6NVaQEFm+LYYMlb54271p0avrVQFJkj6Ycw280U2EzYFTsalRo/Z39q+9fl5fqvoZJUrE5YySdtPufPPstpFNik2PrqpFXzRv+6+Hs5Y7PLTF10gKQMY7Gd/3akZpn4aeVRACIredGhodhFSBAE4WrlLnRlWWHVLscot5G+AkF+jnqaJzKPM3zjq7Sd3wyL3czaAVsY2WQ043Z+QMPfarExcR0Dqw/G18mfpScWk5h7Bp3KCQUF66Xt9nyd/XDXuhPlWxNFgUPpBzDbzZjtZuyKHUmS8NJ50SiwCe83/xAfJx9+PDiL/6vzHBsGbuOh0M4lcqnV003H8IH1cHPWkF9g46sFcaRlm4r9eW6mwGJj2uID5JmsuDppeKZHDVTisrIgCMI1yl3oxh5PvTLS694ijH3Jexi2aii9l3Yh2D2EnUNiGaQfwktrn6H1vCYcSjvAsFrP4KpxY+6x37iQfw5ntTMKChbZDEAFlwA8dB7ofaJQSSoOpMVRYDdhsVuwK3ZkxVH0onlQS75sP4UwzyqM3/0R7Sp3YPuQvQzQP4ZKKtmXOsjPjdf61UWjVpGWXcCE32NJzSqd4JVlhVnLjnAuNR9JghcfqUWgT8nt4CQIgnC/KlehqygKK3aeQUHBOdjAm7se4/k1T9M6pA17Hj9Ii6DW9P2rBw8v7kCyMZkX670CisSPh2aRYkzGReOCgkKBvQCAILcgPHSeVPOujkbSEpcaQ741H6tsQ1Zk7IodF7ULLYNaMavzT9StUJ+3Nw8nxKMSu4fG8ny9l3FSO5Va/6tX9ub1/nXQalSk5xQwcW4MKaUQvPPXGthncOwgNKhDJLWrilKPgiAIN1KuQvfA6RS2pf/NFrc3iZVm80TNYewcHENFt2Daz2/BgL97A/BGgxHkW/OZETeVjIJ03LRuyMiYbCYkJCq5V8ZT50W4VyTOKmdiUvaRY8nGLtuRFRmrbEGn0tEmpA1zeiykfehDvL7hJUw2I1sGRzO66fv8f3t3Hh9ldS5w/DeTfSMkLDGsAcEniOwosol4rUoFimJbl9rWItXbe6lapVp6Qdu6IXWpVUSvy9WCtC6IRW7ElUUFBCmCYI8ISCCEIAGSTBJmkpm5f7yDnzDMJGM177yT+3w/Hz+YM2dmzjPnvOd59zcnNT63ZzyjVwduuMy6eUZltZe5izZRcaT1jvGu317B4jcMYF2a9Z0zu7fadymlVKJrE0m3tqGWJz6ez9Q3xrA35S3GZ/47a658H6/fy9CF/Zn+xk/olNmZm4fdyoHach7cNI+qY0fJTsnGj5/ahlpcuChq14t2qbkU5fYmKyWLjyo2cNhbGTpjOYAv4CPZnczYruN4ZcpyJveZyn+8PZ1PDm1l+aVvct+4BynILIj3z8HpRfnc+P1BpKa4OVLj5Z6FmzClR77171m5uYwFS7cB0KdrLj++sFgvD1JKqWYk9HW6lfWVPLl1Ac9ue4qBeWcxoPpmcgO96Vy8kX7P9MLT4OGcbucy4pSRzP/4YTZWfEiKO4WclBxqGmrwNHhw4eLU9n04VH+Ibjk9CAQCbDiwjsZAIymuFILBIF7/MZJdyYzsMpo5I39PaU0pM965ni5ZXXluwmIGdx4a75/iJMU987jp+4N46KUtVNf6mLd4M1PH9eaiET2+cWIMBoMsWb2L5Wv3ANYdsmaEdmsrpZSKLiGTbmn1Hh7Z9DAvf/YCk06dwrJLVlCysppFyY+wPn027PRzce/J9MvvzyObH+TdvW+T6k4jJ7UdNb5qGgINuHFzWn4xB2srKMzqAsEgH5avxR/0k+pOJRgMcix4jCSSGN3lHH4/5m6qvVXcuvpX+AIN3D1mHud2P8/RW3bSI4/ZPx7Oo69spbyyjhdX7mTHviqundiPzPSUf+kzGxoDPFPyKeu2Wdfinl6Ux5xrR+Kt97aZ52oqpVRrSaiku/Po58xYOY+SHSX8qN9PWXP5h6QnpzNn9Rz+VrYQ0uC8zlMZXtSXhzc9wKs7l5CRlEG71FyqfVX4fF7cuOnf8QzKPeV0SLdO+FlX/gH+oJ80dzqNgUbq/fW4cDOycDT3nnM//qCfu9bdwY6jO5g1YjZT+kxt9bORvy1dOmYx+yfDee51w7rtFWz+/BCzn/qQiaOKGDOgMOat02AwyCe7D/Pyqp2UVngA68lB0yb2IysjBW+9tzWMJGcWAAAOpUlEQVTDUEqpNiGhku7GAxsYVDCIu0beh8dbz+z3buO1Xa/iJoVevu+RnpTGe5VLeOvgMbKSs2mX2o5qXzX1/nrcuBnYaTDlnv20S83Fle1m/YG1oXsmp+MP+Kn31+HCxfCCETw4/s9kJGdw74d3smrvu9w07BaenbCY1KTEu3F/emoy0yedTt9uuSx+ewdHarz8ZYXhtQ++4Ltn9+ScQYWkJJ/8RKPjTOkRlqzexY59VV+VTRxVxCVje5GclBgrH0op5QQJlXR/WHwFVa4vuXbpNazc+w7ZqTncOnw2S9Zuw6S+QsDVQI67HalJaVT7rAThdrkZ0nkY+z1lZCRn0C2nO+vL1xLASrbegJd6v/Ug+SGdhvHo+U+Ql57PQx/N4wWzmGkDruO+qx4gOzWxnwXrcrkYP7QbxT3zWPbBF6zfXsGRGi+L3vyMl1btpHunbLp3zqZb52zSU5Mor6yl/FAdZYdqT7jDVZ+uuUwd1xvpkRfHaJRSKjElVNL9zepf8+SWx+mU0Yk/jvsTO4/s4N6Nd+JPaiA5mE1majo1DdWAlWyHF5zFPs8+kl1J9MgpYsOB9daWbVKGdY/kULI9o8NAnrjgGQqzu/D4x4/yxJb5XNL3MtZcsYHOmfF/gMC3qbBDFj+f1J9Jo4pYvnYP67ZV4PX5+bysis/LqqK+r2dBDpec05sBvfMdfRxbKaWcLKGS7uiuY7jwtPNZ8c+3mLnqRhqDjaTRDhfJNLo9eBqsZHvWKWez31NGIBjg1NxT+WD/ewSCQTKTM/D5GzgWqCcQDCB5/XjmooX0bFfEok+f4/6NcxnddQwlU9+hV25sz99NVIUdsrh24ulMGduLz/YeZe9BD/sOeth70IO3MUBhfiaFHbLo0jGTosJ2nN4zT5OtUkp9QwmVdHcf3c2dJXfQGGykc0YBNT4P9Y2hLVvcjCgcSUXdAbx+L33a92HVvpUEggEykzNpDDRyzH8Mf9BP79xTeW7CX+mbdxrLdi7lR//7A7rn9GDRxS8wsNPgOEdpr465GfokIKWUsklCJd3V+1ZSkF3AkfqjHKyvCJW66JY8kPScOuoaa+mT25e39775VbINBIN4/V4ag410z+nBwgl/o1/H/qzZt4oZ71xHIBhk7jkPMK77+LjGppRSqu1LqKTr8/soqykDwIWbvMZifC4PaRk++rYX3tzzOluCH5ORnIGbJI7562kMNnJKViHPXvQ8QwqGsfXQFn647BJ2V+1i1og5TO5zScJc/qOUUiqxJVTSPXKsEjduziocwZ5DlXj8Hjom9aS0bh27vvgnGckZpLhTqW300BhopGNGJ5684FlGdR3DF1W7uf7NabxXtppfDf81P+r3k4S8/EcppVTiSqhNvN+efTtDC4fyZV0lSXWn4HGX8wXvkexKIS8tn4ZAA1U+657Kz3/3RbZfs5O+ecKsNTO56OXx9Gnfl3VX/YOfnTFdE65SSinbJVTS9QV8FHcqZm91KfuSV+PCRce0jjQGGjjsrSQtKY0F5z/FZ9NKObvLKOZtuIcxi4fjwsWayzdwy5m3kZ2SHe8wlFJK/T+VULuXH//4Mdbuf58kUkkN5NOYVM0h75ekJ6Vz56i5XDPgWnx+H09tfYIHP5rH2K7jWHHZSopye8W76UoppVRiJd1RXUaz68gXVNQdwO8+TLI7hduGz+GGYTcTJMgrO17invV/oFdubxZf/BIDOg2Kd5OVUkqpr8SUdEVkCPA40B/YAVxvjFnXmg2L5P2yNVTUl+HCzZkZl7P0p/NJdiezau+7/GHd7bhxcf+5DzO22zi7m6aUUkq1qMWkKyLpwDLgLuBJ4GpgiYgUGWN8rdy+E/TKOp0ybzZneKdz04XD2XZoK39Ydwf7akqZNWIOk06dondNUkop5VixbOmOBwLGmMdCfz8tIjcBk4CXW61lEQzxX0eNdz/p7Y8wf9dM1u5/n1vOvI0ri68mJelfez6sUkopZZdYkm4xsD2szGDtam4x6bpcLtzfwjnSnvoGVm77J9vS/0ql+wN+2fGXPHz+o2SlZH3zD48Dt9t1wr+Jqq3EARqLE7WVOEBjcSq7Y4kl6WYBdWFldUBmLF/QoUPWt7LL92hZFXtcq0lLSuGT67fTs0PhN/5MJ2jfPjFXGsK1lThAY3GithIHaCxOZVcssSTdOiD8jviZgCeWL6isrP1WtnTbZyTx0JRZ9O6eT25SMocPx/T1juV2u2jfPoujR2sJBILxbs6/rK3EARqLE7WVOEBjcarWiCU/P/r9IGJJup8C/xlWJsDzsXx5MBjE74+lZsuGntaJ/PxsDh/24PcndkcfFwgE20QsbSUO0FicqK3EARqLU9kVSyxJ9x0gTURmAAuwzl4uAFa0ZsOUUkqptqbFHb/GGC8wAbgCOAzMACYbY2pbuW1KKaVUmxLTzTGMMVuAUa3cFqWUUqpNS6gHHiillFKJTJOuUkopZRNNukoppZRNNOkqpZRSNtGkq5RSStlEk65SSillE026SimllE1cwWDbuIWXUkop5XS6pauUUkrZRJOuUkopZRNNukoppZRNNOkqpZRSNtGkq5RSStlEk65SSillE026SimllE006SqllFI2iekh9nYSkSHA40B/YAdwvTFmXYR6NwIzgRzg78B1xphaO9vaEhEZA9wPFAOHgPuMMY9HqLccOA/wHy8zxmTb1c5YiMhM4C7A16R4gjFmTVi9K0L1OgMrgWnGmAq72tkSEbkKa3w1lQk8aYz5eVhdx/aLiJwFLDXGdAn9nQc8jdXeKuB3xpinorz3fOAhoBewCauPPrOl4Se3JTyObsAjwFigAXgRuMUY443w3pjGpF0ixHImsA6ob1LtbmPM3RHeG9O8Z5emsYhID2B7WJU0YLcx5rQI73VEv0Sbf+O9rDgq6YpIOrAMq8OeBK4GlohIkTHG16TeRKyEOx6oABYDvwdutr3RUYQ69u/ADKz2DQbeEpGdxpi3wqoPBsYaYzba3MyvYzAwyxjzx2gVRGQgsAC4ANgC/BmYD0y1pYUxMMYsAhYd/1tE/g34C9b4Cee4fhERF3AN8ADQ2OSl/wY8QAEwECgRkQ3GmC1h7y8AlgBXASuA32CNz2Gt3/oT2hEtjoXAJ0BXoD2wFJgN/FeEj2lxTNqhmVgGAyXGmIktvD+mec8OkWIxxpQC2U3qnAJ8BPwyysfEvV+am3+B64njsuK03cvjgYAx5jFjTIMx5mmgEpgUVu9q4CljzGfGmCqshXKaiCTZ3N7m9ASWG2MWGWMCxphNwLvAqKaVRKQz1lbhJ3Fo49cxBNjcQp2rgFeNMeuNMfXArcD3QjE6johkA88CvzDG7At7zan9Mgu4AWuCBr6KYwpwuzHmmDHmQ+B5YHqE918KbDbGLAtN6HcCvUXE1qRL5DhSgVrgzlAcB7BWkEZF/oiYxqQdToolJNb2xTrv2SFaLE0tAF40xrwe5XUn9Etz829clxWnJd1iTt6NYbB2uTRXzwC5WGvHjmCM2WyMufr436E1r7HAx2FVhwA1wGsi8qWIvC8iI21saotEJBM4DbhBRA6IyKci8rMIVU/oF2NMJXA0VO5Evwa2GmOWRnjNqf3yNNZa+4YmZX2BBmPMriZlkZYbOLmP/MDOKHVb00lxGGN8xpiLQ8n2uEmcvMx8nTFph0h9AtYYGi0iu0WkVET+KCJpEd4f67xnh2ixACAi5wGjibznwTH90sz86yLOy4rTkm4WUBdWVod1zK25esf/P7yeI4hILtbuo49C/zaVDqzFWrvshrV7rSS0C8cpCoD3gceAHsDPgQdEZEJYvVj7L+5CW4czgN9FqeLIfjHGlBtjwp9SksWJxw0h+u/uiD6KEsdXRMQlIg9jTXz3RKgS65hsdc3E8iXW8n4GcC7WFm2k8eaIPoGW+wVrF+v9xhhPlNcd0y/Hhc2/7xLnZcVRx3SxAsoIK8vE2v/eXL3jP0K0gRA3ItILeA1rDemHxphA09eNMa8CrzYpekxEfoG1gC62raHNMMbsBsY1KVojIn/B2k1T0qQ81v5zginAnmgnqyRCvzTxdX53x/eRiGRgHWcfAIwzxhwMr/M1xmTcGGMmN/lzl4jcDdwN3BZW1fF9AiAi3bF+8yuj1XFav4TPv0A/4rysOG1L91NAwsqEk3e9hNcTrLPQ9rde074+ERkKrMc6CD8ldJwzvM5lIvKDsOJ04JgNTYyJiAwVkfCJIlIbT+gXEekI5IfKnWYS8EK0FxOhX5rYAaSEzjI9LtJyAyf3URLQJ0pd24lIPrAKa9yMDE3ikerFOibjQkTyRGSeiOQ0KY7WvljnvXibCKw0xnwZrYKT+iXK/Bv3ZcVpW7rvAGkiMgPrYP3VWLsrVoTVWwgsEJGXgb1YZ54uCt+KjKfQmW+vY+2KmdtM1WzgXhH5BGtA3Ii1dvVG67cyZh7gdhH5HOtsvvHA5Zy4RgvWFuAqEXka2Ii1W7AkdGzXac7GGmPRJEK/AGCMqRGRV4F7RGQ61jGnK4HvRqj+CjBXRC7F2gL4DbAP+Idd7Y0mdObsEuAAMNUY09BM9VjHZLxUYZ2I4w4loZ7Ab4EnItSNdd6Lt7OxDrk0xxH9Em3+dcKy4qgt3dC1eBOAK4DDWMfcJhtjakWkRERmheotA+YCy4FSrJN1Zsan1VFNAzoBs0XE0+S/u0RkgYgsADDG/A/wJ6wBchSYjHVNm2OuOQ5dl/YDYA7WyUXzgWuMMZvCYtmMdRbg08BBoAvW5QeOElpj7QaUh5UnVL+EmQ6kYE0KLwMzjTHrAURkloiUAIROUvoecDvWGbLnA5e2cBzPLiOxJufvAEeaLDOrwbrGWkS2QfNjMj5NP1FoA2ASMAjrGtH3sK45/hOcFEvUeS8OTW9OEWHLDDi2X6LOv8R5WXEFg05Y1pRSSqm2z1FbukoppVRbpklXKaWUsokmXaWUUsommnSVUkopm2jSVUoppWyiSVcppZSyiSZdpZRSyiaadJVSSimbaNJVSimlbPJ/RJl3Uvh6lx8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e529d814a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 5))\n",
    "plt.plot(population_x, population_y)\n",
    "\n",
    "for x_start, x_end, y_start, y_end in random_lines:\n",
    "    plt.plot([x_start, x_end], [y_start, y_end], linewidth=1, c='g')\n",
    "\n",
    "plt.title('Population vs. linear model predictions');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot above clearly shows that a linear model will make prediction errors for this population. We may decompose the prediction errors into bias, variance, and irreducible noise. We illustrate bias of our model by showing that the long-run average linear model will predict different outcomes than the population process:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e529da86a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 5))\n",
    "xs = np.arange(0, 20, 0.2)\n",
    "plt.plot(population_x, population_y, label='Population')\n",
    "\n",
    "plt.plot([avg_line.x_start, avg_line.x_end],\n",
    "         [avg_line.y_start, avg_line.y_end],\n",
    "         linewidth=2, c='r',\n",
    "         label='Long-run average linear model')\n",
    "plt.title('Bias of linear model')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The variance of our model is the variation of the model predictions around the long-run average model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e529e95d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 5))\n",
    "for x_start, x_end, y_start, y_end in random_lines:\n",
    "    plt.plot([x_start, x_end], [y_start, y_end], linewidth=1, c='g', alpha=0.8)\n",
    "    \n",
    "plt.plot([avg_line.x_start, avg_line.x_end],\n",
    "         [avg_line.y_start, avg_line.y_end],\n",
    "         linewidth=4, c='r')\n",
    "\n",
    "plt.title('Variance of linear model');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we illustrate the irreducible error by showing the deviations of the observed points from the underlying population process."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Go9S3OGjucANQ1WCnsqaNBTMSd6rcQF778BgBINeaxvI5E+MdTkhCHR5ZAmyLZiBCiMjz+vz8/rndON1erBkpfOeGxRTlW1kwoyDkXnHvTW6L87N4ZdMx6lscfabFFeRmJFQlvFB0Oj28u8OoM3LBstKEnubX25A9baVUFjAbuE0p9QjQAvxCa/2nUA5gMpkwD7MtzGZTn//F0KTNwjPa2+updw5TWW2UGf3sFXOZMD78TWnHWdO485PLqKxuw9nl43+f3AUYvxDGj0unpcON3eWh3dHFuASfedHbW1ur6fL4SU+1sHZ5KRZLdM6BSJ9joQyPFALvA/cDHwPOAJ5TStVqrV8a6sX5+VZMQ1zoGIrNNjquUseStFl4RmN7bT/QwPMbDgNw+TnTWXvm9GG/Vx4wuXg8nU4PL244wuHaDqYVjeMbNy7jBw+up62zi9/+aye//PdzGT8uIyLxR5Pb4+ON4DS/i1dOZXLJ+KgfM1LnmCkQCAz9rH6UUv8PSNNaf2Go5zY2dgZG0tO22ay0ttrx+8OPcyySNgvPaG0vt8fHHQ9spKndxZTCbL7/qeWkpVgi8t7OLi91rW4m2dLJTEuhorqNex4px+P1U1aSwx2fWEZqSmIPNazbUsVfX9aYTSZ++ZWzyM+N3i+a4ZxjeXnZg/Z0QxkeWQpcpLW+p9fdGYAjlIMHAgF8vlCeOTi/P4DPN3p+oGJB2iw8o629nnvvME3tLixmE5+7Yh4Wkzliny8zLYVlc2w0N3fi8wWYPimHz14+l/uf3kVldTuPvrqfmy9WETlWNPj9AV4Kbie2Yu5EbNnpMfneR+ocC2V4pBP4oVKqAngSWAPcAKwa8dGFEBFX3+rsSUprl5dSUhD9oZ/T50zk6MqpvLDhCG9urWZGcQ5nLyiK+nGHo3x/A/XB2TCXrJgS52jCN+TfMFrr/cB1wA+ADuB/gVu11uVRjk0IMQz/fP0AXp+fXGsaV549/HHscH303BnMnWaMDf/tFc3R4x0xO3ao/P4Az7x3CID50/OYUjguzhGFL6R52lrr54DnohyLEGKEdlQ2sa3CKAJ17ZoyMtNjV6nCbDbxhSvn8eO/fEhTu5v/eXInP7r19IRacLNp33GqG+0AzJueh8PlSaj4QpHYVwuEECHz+wM8tu4AYMytXjlvUsxjGJeVxpc/uoAUi4nGNhd/enEfw5nsEA0+v59n3jsMQHqqmcfWVXDXw1uSbgm+JG0hRokP9hzvKXx049pZI55qO1zTi3K44YJZgDF+/Fqwtke8bdx9nOPNRvu4PcbmDjVNDvYk2bZqkrSFSHIOl4dtBxp4+r2DACyZVRD3wkdrlpSw4jRjWfj/vVnBn1/aQ2OrM27xeH3+nrHs6UV9x7ET4++A0EnSFiKJOVwe7nm0nPue2ElDqwuAq86J3cXHwZhMJm65ZA4FuRn4/QHe3V7HHQ9uiFvifnd7DY1tLkzAjRfMojjf2LQ31KJZiUTqaQuRxCqq26hqsPfcnlWamzAzIjLTU5g/I4+3thr1PXx+WL+rhivPKYtpHJ1OD0++Y/wVcsbcQmaW2rjz5mVU1rSFXDQrkUhPW4gkNrMkl/HZJ+p9XLs6tglxKJedMZXeJTc6HN6Yx/DE25XYXV7SUy18PNg+WRmpYRXNSiSStIVIYulplp5CRMtmT2BmqS3OEfVVYMvkni+sZNokY3uyN8qre6YkxsKh2nbe2Wb09K88exp5OYlfF2UokrSFSGIf7qunqd2oaX31eTPiHM3ACmyZ3PGJZUybZAzb/PG5PdQ22Yd41cj5AwH+8uJeAsBEWyYXnj456seMBUnaQiQhh8vD9ooGXtxwBIBFZfkxWa4+XKkpFr780flkZ6bicHu59/EddDqjOz/6hfWHORYc729sd9Ia3LAh2UnSFiLJdM8YufdfO3suQl5yRuLX0CjIzeSr1yzAYjZR3+rkf57Ygcfrj+gxuvesPHCslWfeP9xzv98PG3bXRvRY8SJJW4gk03/GSGFeJrMnJ9ZY9mBmT7Zx62VzANhf1cZfXzZWTEZig+DuX2a/fXwHv/jn1j5lUFMsJlbOS8wCVuGSKX9CJJmZJblMyM2goc2Yl33hssnsPNjEzJLkmL521vwi6pqdPL/+MOt31ZFiMVFZ3UZ1o2NEGwT3/mXm9QUwmeBLV82ntqmTlfOKKLCFv2tPIpKkLUQS6gz2SC1mE29sOUZtszOpdkS/+tzpNLe7WL+rjne2nxi26L9BsMPloaK6LaRfSDNLcrFlp9Ha2QUYs0WMzXqTY8PeUEnSFiLJbK9sxOk2dhbx+QPUNhurDJNpR3SzycSnLzuNQAA27K7rub+kIIuiPCs7Khspzrdy3xM7qGqwn/IXUmOrk/d312LG1JOw504bzxUxLEsbS5K0hUgy1b3GsyfaMkixmKlpMoYWkmlHdLPZxGc+chpwInFbM1P5zePbqW1ykJ+bQVNwCGiwX0iNrU7u/MNGvL12hCkryeHLVy/AHKeCWdEmSVuIJOL1+Xlvx4nhhBSLma9fu4jaZntSLMnuP9zRnbjTUs28va2G/cfaep7b1OYiPzedpjb3oL+Q3t5R3Sdh5+ek883rFse0jnisjd5PJsQotEU30O44McOipslBbbM9KYZEumd39B/uMJuN4lJlxbk8/KrumQaYmW7hprWzsVhMA/5C2nqggfU7jve57+vXLhrVCRskaQuRNBwuD8++b5QXzUiz4OryJdWQSO/ZHQMNd5yzsIhpk8bxu6d2crzFidPt474ndlJSYKWsJIfifCupKWYqqtupqG7tqWpoNpsoKx7Hpy6ZQ1FBdlw+WyxJ0hYiCThcHn78lw+pDyaqa1eX0eHs4qx5RQk/JNJtZkkupROsPT3tgX7ZlE7M5vablvLCxiNsO9BIY5uL6kZ7zxZh/anJNj5xsUro1aCRFnLSVkoVAjuBT2utn49eSEKI/iqq23oSNsALGw/T3N7F5n0NSTPNLysjldtvWnrKkqgOl4dfPbaNqgY7eTnpfR6zZafh9weYVpTDzJJcZk+2Mas0N2479MRLOD3th4D8aAUihBjcpLysnq+zMlJobjemtiXTND84URJ1ML2HUJrb3X0uRCbLL6doCylpK6W+CNiBY9ENRwgxkPL9RjnT1BQz/3njEv7w/J5TDjMkq/5DKP/+sYVJMzMmVoZM2kqpWcC3gDOA8nAPYDKZMA+zwkl3nWCzeWz9+TMS0mbhSYb28gcCvLWtGoCzF0xiWnEOd35yGZXVbZSV5GKNcTKLZpuNs6ad9NkK87OGfmECi3R7nTJpK6VSgEeA27TWzUqpsA+Qn28d8ZiTzTZ2LjJEirRZeBK5vcp1PfUtxqrHj66ZTV5eNnnA5OLxcY0rWm2WCJ8tGiLVXkP1tL8PbNNavzjcAzQ12UfU07bZrLS22vtU7BKDkzYLTzK01zNvVQDGSj9bpoXm5s64xpMMbZZIhtNeeXmDT10cKmlfDxQppa4P3s4B/qmU+m+t9T2hHDwQCODzhRTnoPz+AD6fnBzhkDYLT6K2V3O7i60HGgBYvbgkoWJM1DZLVJFqr1Mmba31nN63lVKHga/KlD8hYuOd7TUEAmDNSGHFaaOrWp0YHtkEQYgE5fX5eXu7sSntOQuLSE2xxDkikQjCWhGptZ4WpTiEEP1sr2ikLVhqdPXikjhHIxKF9LSFSFBvbTWm+c2dNp7CvOSe9iYiR5K2EAnoeIuD3YdbAOlli74kaQuRgN7eaoxl52ansXhWcixRF7EhSVuIBOPx+nhvp7HRwXkLi0mxyI+pOEHOBiESzGbdQKfTg8kEqxYXxzsckWAkaQuRYN4MXoBcVFZAXk5GnKMRiUaStogbh8vDjspGHC7P0E8eI6rqO6moMvZJXL1ELkCKk8nONSIuBtsvcKxbV14FQEFuBvOn58U5GpGIpKct4mKg/QK7jdUeuMPlZcNuY6PaNUtLErpcrIgf6WmLuBhsv0CHy8NdD2+hpslBcX4WX792ETVNdmaWjP4i+O/vqsXt8ZGaYubchXIBUgxMkraIKYfLQ0V1GzNLcnv2C0yxmHn8rUrqW5zUNtpptRtLt2uaHPz4Lx/S6fKO+iEUfyDAunLjAuSK0yaSnTk6P6cYOUnaImb6j2NfcdY0Xth4hKPHB68P3enyAsYQyoGqVhbNnBCrcGNq7+EWjjc7ALhgWWmcoxGJTJK2iJn+49j3P7O757GJ4zMpnWClON/Keztrae3sItVixuPz9zznsXWVpKVYOG3a6LtA130BckZxDtMm5cQ5GpHIJGmLmJlZkktxfhY1TY6THvP5/JTvb6R+gpM7P7GsZzPX1k43j752gL1HWqhrdvDLx7Zxw/mzWLu8dMTb2CWKxjYn2yqMjXvPXyrT/MSpyewRETNdXn+fGRHZmUafIT83naZ2N2D0wGub7SyYUUBWRirFBdl858YlfO+TyymdkE0gAP944wCPvLofb69eeDJ7Y0sVgQCMy0rl9Dmy0YE4Nelpi6hzuDzsPdLCs+8fpqrBjskEN14wi7PmT6Kypo2iPCv3PbHjpJkkvc0ozuHOm5fy4LN72FbRyJtbq2loc/K1axYk9eYATreXd4IbHaxZUpLUn0XEhiRtEVUOl4e7H9lCdaMxJGICvnTVfJYHe5QLZhgV7LpnkpQVDz61LyMtha9es4D/e7OCVz88xq6DzTzwzG4+dYniUF1HUk4LfG9HLU63jxSLiTVL5QKkGJokbRFVFdVtPQkb4KwFk3oSdu/pf1kZqT0J/FTMZhM3XDALa0YKT717iK0HGtFHW3C4fUk3LdDvD/Da5mMAnDlvErnWtDhHJJKBJG0RVe4uX8/XmekWbjh/JjDyZeyXnzUNp9vHy5uO4nAbx+heWRlK8k8EWw800NjmAuCi5ZPjHI1IFiElbaXUdcB/AZOBI8B3tdZPRzMwkfwcLg9/f+MAYEzpu/2mJVgzjd7kQMvYw0m2JpOJa9eU0e7oYv2uOgBs2WkDjocnqpc/OArAnCk2SidmxzkakSyGnD2ilJoN/Bn4jNY6G7gNeEwplRzdGRE3j79VSVtnF6kpZr5x3SJs2SfKjHYvYwcGvfg4FJPJxKcvO40FM4x52+32Lg7XdfQ8nsg1TPYcbqayph2AhlZnQsYoEtOQSVtrvR8o1FqvV0plA0VAB9AV7eBE8tJHW3h7mzEr4upzplM4vu/GtFkZqdx+01K+cd3CEY1Dm80mvnjVfEoKrPgDcP/Tu6hvcfQMv/z28R3c82h5wiXFJ9+u7Pm6qd3dp2CWEKcS0vCI1rpTKTUdqCA4AUBr3R7Ka00mE+ZhzgbvntMr1c5Clwht1uX18ZeX9wEwpTCbS1dOwTJAPOOsaSyeNfJl6dlZqdx23UL+688fYnd6+cU/tnLN6hl9hl8O1bWzsOzkPw7j0V5H6jo4WHviL4LJE63MmmzDYkmO8zwRzrFkEun2MgUCgZCeqJRKwUjY5wLPAldqrdcN9bpAIBAYLSvXRGgeeXkvj722H7MJfnXbKmZOtsXkuBt31fLTP28CICs9hfzcDI7VdzKtaBx3f+XchCjCdLzZwY//uIGjxzuZlJ/F569ewGnT8xMiNpFQBk2aIc8e0Vp7g1+uU0o9AVwNDJm0m5rsI+pp22xWWlvt+P2h/XIZ6+LdZi0dbp56swKAi1ZMIc+aQnPz4AWhIsnldPd87XB7WV40juvOL6OsJJcup5vmXo93i2V7NbQ6+c/719O9kHPVomLKJmUPGluiivc5lmyG0155eYNfmB4yaSulLgO+qbVe2+vuNKA1lIMHAgF8vqGfdyp+fwCfT06OcMSrzZ565yBdXj/WjBQuXzk1pjFMn5RDSUFWz7zw93fWcd6iEjJSU4aMIxbt9daWKnqvvO+wu5P6vJafy/BEqr1C6QOXA8uVUjcrpczBJH4Z8PcRH12MKrVNdt7dXgvAR1ZOi/kil6yMVG77+CIuWzmZvJx0fP4A9z+9i06nJyFmkqSl9e0jTcq3xikSkcyG7GlrreuUUlcAvwF+B+wHrtZa74t2cCK5PPnOQfyBAOPHpTNxfAYOlyemidvh8vTUMJloyyDFYqKp3cWDz+6mpcNFdaMjrqsme88QKbRlsHT26KwNLqIr1NkZi3hXAAAYdklEQVQj7wLLoxyLSGKV1W1s0Q3BWwH+58ldMU+QvRfs1Le6WLushNe3VLPrUHPPc+K1anL/sVa2VzQBcNHppVx59vSkWW4vEouUZhUR8eQ7BwHIz0mnpcOYwt9/w95o679g56pzprNyXmGf5wx3Ic9I+AMBHltnrAydMjGb686fJQlbDJvUHhEjdrCmnb1HWgC45rwZvPTB0VOWWY2W7gU7vasFfvLiORw53klNox1rRgpfvnp+zBPmu9trOBScl339+TMxyxRYMQKStMWIvbDhMADFBVbOmDeJRTMLhiyzGi39qwWmp1n40tXz+clfP8Tu8vLnl/bxnRuXkGKJzR+ZrZ0uHnl1PwAZaRamThoXk+OK0UuGR8SIVDfa2XrA2CrrsjOnYDaZehJnogwBlBRY+fRlpwFwoKqNfwSLWMXCP16vwBecm+vq8slydTFikrTFiLy44QgA+TkZrDitcIhnx8+K0wq55IwpALxZXs19T2ynsdUZ1WMeqm1ns67vuR2P8XQx+sjwiBi2xlYnH+w5DsClZ06J2ZDDcH18VRmV1W0cqGpj24EmdlZu4GdfOuuUq8+Gy+P18cfn9xAIQOH4TK5bU4aaMj5h/voQySuxf8pEQnt501H8gQA5Wamcs6Ao3uEMyWw2MbM0p+e2zw8vbzwSlWM99c4hapscmEzw2SvmsmT2REnYIiIkaYth6XR6eG+HsfrxwtMnk5aaHBvSrllcSu8/CD7UDREfJtl7pIVXNhkbHFx6xlQZEhERJUlbDMu722vo8vpJSzWzanFJvMMJWYEtk7s/v5JVi4pITTHT1tnFD/+wgU5HZJa3Vzd08rsndxIASoJzxYWIJEnaImw+v583yqsAOHt+UdKVFS2wZXLLpafx5avnYzaZOFrXwX//bTNNwf0ah6ulw81vHt+Ow+0lOzOVr16zgNQU+RETkSVnlAhb+f5GmtuNUqJrl5fGOZrhWzSzgM9fNReL2URtk4O7HtlCdcPJZWRDKTblcHn57ePbaW53k5Zi5rZrF560W48QkSBJW4TttQ+PATB/Rh5FSV6pbuW8SfzgM2eSnmqhpcPN3Y+U96qhQkjblh2r7+Qnf/2QY/WdmEzwhavmyTi2iBqZ8ifCsvdwMxXVxgKRi5ZPjnM0kbF0zkT+86Yl/Pqx7XQ6PfzuqZ0smpnPijkTSbWYT7lr/Hs7ann4VY3H68dsNnHB0hJUjHbqEWOTJG0RMofLSGgAKRYT04tGz5LsspJcvnfLcv7y4l72HTUq8m2vaCIz3UJ+TjpN7e6exTEOl5cP9h7nne01HAnu/m7LTiM1xcxrm6vYe6QlbuVfxegnSVuEbHtlIw63sQ2R1xfgYG17zEucRtNEWybfuXEJD7+ieSu4k7zT7cPp9pGeaqbd3sXtv9+I0+3tWZoOMG96HmcvmMSDz+4B4lf+VYwNkrRFyOqaHD1fFxdkjcpxW5PJxJyp43uSdje3x4/bc2KvsBSLmWVqAucuLOK0qeNxur2UTrDGpbqhGFskaYuQ+P0B3t9VB8Dimfl89vK5o/bP//nT8yjOz6KmyUFxfhafvXxuz7i2xWIiLcWMmjK+z1THgcrCChENkrRFSLZXnpjm97HVM0d1UsrKSOXOm5f1ScDTinJCep0MiYhok6QtQvJmeTUAc6bYKClI7ml+oZAELBJVSElbKXUO8CtgDtAI/Fxr/ftoBiYSx/EWR88+i2uWJu9imuFyuDxUVLcxs0SGPUT8Dbm4Rik1HngWuA8YD1wL3K2UWhvl2ESCeGur0cvOzU5jyayx1fsMZXGNELEUyorIqcALWutHtdZ+rXU58CZwVnRDE4mgy+Prqea3alFxwtfMjrTeO7zHeqNiIQYy5PCI1nobcHP37WDP+1zgb6EcwGQyYR7mz7nZbOrzvxhapNtsy+4G7C4vZpOJNUtLsFhG1/diqPaaPcXG5IlWjtXbmTzRyqzJtlHXBuGSn8vwRLq9TIFAYOhnBSmlcoEXgA7gI1pr/xAvIRAIBEyy+3TS+s5977DvSAtnzp/Ed289I97hxEWn04M+0oyampd0FQ1F0ho0aYY8e0QpNR14HqgErg8lYQM0NdlH1NO22ay0ttrx+0P/5TKWRbLNjh7vYN+RFgDOmT+J5uaTK+Alu1Dba/pEK11ON81OdwyjS0zycxme4bTXqbbAC3X2yFLgZeAR4NuhJmyAQCCAzxfqswfm9wfw+eTkCEck2uyNLcYFyAm2DOZMHT+qvwdyjoVP2iw8kWqvIZO2UqoQI2H/Smv9sxEfUSQFp9vLht3GCsjVi0swyxCXEAkhlJ72Z4AJwPeVUt/vdf+9WuvvRicsEW8f7DmOu8uHxWzi7IWJv2mvEGNFKLNH7gLuikEsIkEEAgFe22xsdLBgRh45WWlxjkgI0W1sTboVISnXDdQGK/rtPNgU8d3KhRDDJ0lbnOSZ9Yd6vvb5YcPu2jhGI4ToTZJ2L6Fs4DqaOVwePthTR23jibrZKRYTK+fJmLYQiUKq/AU5XB7uenhLTw3lO29eNqaKA3XX2Ohesp2WYuai00s5b1EJBbbMOEcnhOgmPe2gXYeaqQmO49Y0Odh9uDnOEcVW7xobAGqKjWtWzZSELUSCkaQd5PH0XQHUYe8aU0MlM0tyKchN77n9kZVT4xiNEGIwMjwSZOlXzOWZ9w7R4TT2/RsLO2tnZaQyKd9KY5ubGUU5zJ48Pt4hCSEGMKaTdiAQoHx/Ix/sPc6OysY+j3U4vYBRjvOlD45w1TkzRnVZ0sZWJ7uDGx1csHzsbXQgRLIYs0m7rdPNn17cx86DTT33mYC0VAtenx9fr8IuL2w4yrryaj5xoWLl/ElxiDb61pVXEwhATlYqy9XEeIcjhBjEmEza5fsb+MtL++h0GuPVsyfbOGNuIUtnFZCbbYzrtna4eH1LFfpoK5U17TjdPv7w/B72HG7m5osVaamWeH6EiHJ3+Xhnew0Aq5eUkJoyev+iECLZjbmk/drmY/zj9QMAZKRZ+MRFs1k5bxL9a37bxmXw8dUzeeb9g1TWtPfc//6uOg7VdfCNaxeRn5sR09ijZf3uOhxuLxazicLxmThcnlE/hi9EshpTXar3d9b2JOyZJbn8+NMrOGt+0UkJu7ez5xXRPZRtAswmqGm0c8+jWzje7Bj0dckiEAjwerDOSHqqmT88v1f2QhQigY2ZpF2+v4E/v7gPgLKSHL51/eKQ5iBnZaQwwZYFQGFeFl+6ej5pKWaa2t3c/Wg5VfXJvTFA+f4TdUYcbmPao+yFKETiGhNJu6KqjQee2YU/EKB0gpWvX7uI9LTQxqQrqtuoC/ao65odpKWa+eb1i8lMt9Bu7+Jnfy+nuiE5E7fD5eGhF/YCkJpipjjf+OVUOsFKWXFuPEMTQgxi1Cdtp9vLg8/txusLMMGWwTevX4w1jPHamSW5lE6wAieS2ezJNv7jxqVkZ6Zid3n5zePbaelIvm2oNu07jqvL6F17vH6uPnc637hu4ZiYly5Eshr1Sfvvr++nsc2FxWziKx9dgC07fegX9ZKVkcrtNy09KZlNnTSO265dSFqKmeZ2N/c+vh2n2xuNjxA1B46dGAIpKchi7rQ8FswokIQtRAIb1Ul787563t9pbJl1zaoZTCkcN6z3ycpIHTCZlRXn8oUr52EywdH6Tu5/ehdeX8jbZ8ZVS4ebD/fVA7BqcRF3fGJsFcgSIlmN2qTd0uHmry8bFx7nTLFx8elTonKcJbMn8G9rZwNG0al/vVWZFCVeX9t8DK8vgDUjhevPnyUJW4gkMWrnaT+27gB2l5fM9BQ+85G5mM3R25j2gmWlHG9x8PrmKl798Bib99XT3OFO2LolDpeHt7YaO61fsKyUjLRRexoIMeqE1dNWSq1QStVEK5hI2X+slU17jT/9r11TFpNFMNetmcnsyTYAmoMXJRN16tybW6txdflISzFzwTKpMyJEMgkpaSulTEqpTwOvAgm9y6s/EOAfbxgLaCZPzOa8hcUxOW6KxcyXrp5PrvVE8xTnZyXc1Lkuj4/XNlcBcO7CYsbJpr1CJJVQe9p3ArcBP41iLBHx/s5ajtR1APBva2dFdVikv1xrGl+9ZkFPmdcCWyaZ6Yk19LCuvJp2exdmk4mLV0yOdzhCiDCFmlH+BNwFrAr3ACaTCfMwL3d2J9xQE6/T7eXJtw8CsHzOBOZOzxvegUdg9hQbH19TxmNvVLCjsonXt1RxyRnRuQg6kFO1mdPt5cWNRwBYtbiYwuBimrEs3HNMSJuFK9LtFVLS1lrXAiilwj5Afr71lLU9QmGzWUN63iMv76XN3kVqipkvXLOIvLzQXhdJnU4PG3fX9dz+v3UVZGWmsfaMqWRnxu6C5EBt9vdXjMqGqSlmbrliHnm5spVYt1DPMXGCtFl4ItVeUf/bvanJPqKets1mpbXVjr9XfeuBdDo9PPN2JQAXLi8lzRSguTn2y8t3VDZypO7EcX3+AA89t5uXNhzie7csD2s15nAM1mYdji6eeqsCMGaMmHy+uLRPognnHBMGabPwDKe98vKyB30s6kk7EAjg8w39vFPx+wP4fIN/WIfLw8OvaGNGRKqZi1ZMOeXzo6nQlkWKxYTXF8Bsgu7vUU2jA32khUUzJ8Qkjv5t9tz7h3F1+chIs3DpGfFrn0Q11DkmTiZtFp5ItVfSL65xuDz8918380Fwit95C4vJieOMiJomO97gN8YfAGvmid+LB6riM/2vsc3JG1uMedkXr5giM0aESGJJn7T3HGqmrsXZc7t0YnzH2foXmPrhLaczf7qxSe5LG4+yq9f2ZtHmcHnYXtHA317ReH1+MtMtnLNgdG6XJsRYEVbS1lq/pbUuiFYww+H09B17ifcUu/4FpgpsmXz1moVMKcwmADz43B6a2lxRj8Pu8nDPo+Xc+6+d7DpobNjrdPu49187Enp5vRDi1JK+p13fa/eYwvGZzJsW+2l+/fUvMJWWauHLH11AVnoKnU4P9z2xA1dXdCsCVla3UdVgP+n+RF2lKYQITVIn7S6Pj7e31wKwZFYB379lecLV+eg20ZbJ54MVAY/Vd/KH5/bgD0TvIk5ZSS7WjBN/dUy0GUv5ZYMDIZJbYi3XC9P63XV0Oj2YTSb+be3shE3Y3RaW5XP9mpn8c10FWw808tQ7B/nYqrKoHOtgTTt2l9Gbz85M4ds3LKG22U5ZcW7Ct5MQYnBJ29P2BwK8usnYkHb5nAlJszP6hadP5tyFRQC8sOEI726PfP2t1g43Dzy9u+d2p9NLbbNdNjgQYhRI2qS9o7KpZ+/Gi1fEbpn4SJlMJm6+WDGzJAeAv7y0r88KypHy+f384pHNdDo9dK9DlSERIUaPpB0eeXXTUQBmT7YxvSgnztGEp8vjwxEcuggAf3x+D9WNdi49Y8qIe8L/eusgOyoaAbjlEsX4nHQZEhFiFEnKnvaRug72HW0FSMpKdRXVbdQ0nZj14g8YQyU/eGjTiKbjvfbhMV7cYBSEunB5KectLpEhESFGmaRM2q9+aPSyC/OyWDQzoaaNh6T3Apzx406sTmwObpEWbj0Hu7OLB57Z1VNHfN6MfG5YOytyAQshEkbSDY+02bt6dqW5cHkp5hFWEIyH7gU4lTVtFOVZ+c3j26htMlZ1frivAVfXDj57+WkhLTdvt7v57h8+6JkpoqbYuOrcGbg9PjJSk+7bK4QYgikQxbnCAA0NHcM+gMViIi8vm+bmTjrsXVRUt1FR3cbz64+QmW7hV185e1Tsb+hwedh/rIUt+xt7do/PSLNw0emTuej0KWRlnPwZ/YEAm/Ye559vVNBu7+q5f/y4VFo6PJQUZMkO6yHofY5J8aPQSJuFZzjtNWHCuEF7o0mR8ewuD3c9vIWaJkdPIfGz5xeNioQNRs978ayJLJ41kbKSXB5bV4Gry8ez7x/mjS1VzJuex9TCcRQVWGm3d1HV0Mm+I61UNfQtrTo+O42WDiOBVzc62H24mdPnFMbjIwkhoiQpst6uQ809F+66x3vXLC2JZ0hRs3pxCctmT+CljUd5o7wKu8vLpr31PUNC/c2bnsdVZ0/D2eWlvbOLh17c1/NY8g0cCSGGkhRJ293VtyhUSYGVovzRu2vGuKw0rjt/JhetmMyb5dXsO9pCa6ebhlYX2ZmpFOVnUdNox+7y0tbpprjASlZGKg6Xh+JNx6hptFNcYGVuAtRhEUJEVlIk7Yw0S5/bC8vy4xRJbKWlmNl6oIGqBjulE6zc+7WzGWdNZ0dlI799fAdwogBU99S+792yjPr2LibmpMmFSCFGoaSY8jdveh5ZwZKrFrOJS2O4UW48VfSq1FfVYOfwcWOX+f41u3uvdrRmpLJsTmHUtzUTQsRHUnTFzCYTvuBY9uVnTSV7jOy80p2cu3va3cm595RBWe0oxNiSFEl7/a463B4fKRYTa5aWxjucmDlVcu6u2S2EGFsSPmkHAgHWlRv7Gy6fMzGu+z/GgyRnIURvCT+mve9wC1X1xnzk1YtH5zQ/IYQIVUg9baXUEuD3wDzgAPBFrfXGaAbW7aUNhwAomWBlVqmUFxVCjG1D9rSVUhnAc8CfARtwH/CkUirq4xSdDg/vBTcJWL24BFMS1hkRQohICmV4ZA3g11rfr7X2aK3/BDQBV0Q3NHijvAqP1096qpmz5k+K9uGEECLhhTI8MgfY0+8+jTFU8sRQLzaZTJiHMXJud3l6akOnWMyYzEbhFXFq3bVZuv8XpybtFT5ps/BEur1CSdpWwNHvPgeQFcoB8vOtwxrWOLT3OK7g8nW7y0t9exfLiseH/T5jlc02epf5R4O0V/ikzcITqfYKJWk7gMx+92UBnQM89yRNTfZh9bQn5qYxeWI2x+o7mTwxm4k5aTQ3h3TIMc1sNmGzWWlttYe9mcJYJO0VPmmz8AynvfLysgd9LJSkvRf4ar/7FPD3UA4eCATw+YZ+Xn8ZqSnccfPSPnU0pHZv6Pz+gLRXGKS9widtFp5ItVcoSXsdkK6U+hrwAHAzUAi8MuKjD8Gakcqy4vFSbF0IIYKGHLjQWruBS4EbgWbga8CVWmt7lGMTQgjRT0iLa7TWO4CzohyLEEKIIST8MnYhhBAnSNIWQogkIklbCCGSiCRtIYRIIpK0hRAiiUjSFkKIJGIKBGTRihBCJAvpaQshRBKRpC2EEElEkrYQQiQRSdpCCJFEJGkLIUQSkaQthBBJRJK2EEIkEUnaQgiRRCRpCyFEEglpE4R4UEotAX4PzAMOAF/UWm+Mb1SJTSn1HeCnQFevuy/VWr8bp5ASllJqBfC01ro4eHs88CfgfKAN+C+t9UNxDDGhDNBepwMbAWevp92ltb4rHvElCqXUOcCvgDlAI/BzrfXvI3l+JWTSVkplAM9hJKA/YuxL+aRSaprWuuuULx7bFgN3aq1/Ge9AEpVSygTcCvwa8PZ66A9AJ8b+pwuBl5RSHwZ3bRqzTtFei4GXtNaXxyWwBBRMzM9ibMn4D4w2el0pVQl8kQidX4k6PLIG8Gut79dae7TWfwKagCviHFeiWwJsi3cQCe5O4DaMDgEASqls4Grgh1prl9Z6E/B34HPxCTGhnNReQXKunWwq8ILW+lGttV9rXQ68ibFVY8TOr0RN2nOAPf3u0xhDJWIASqksYDZwm1KqTim1Vyn16XjHlYD+hNED+rDXfbMAj9b6YK/75HwzDNReYCTts5VSh5RSR5VSv1RKpcc+vMShtd6mtb65+3aw530uYCKC51eiJm0r4Oh3nwPIikMsyaIQeB+4H5gCfB74tVLq0rhGlWC01rVa6/6lLa30HZsFOd+AQdsLoAFjCHM+sBrjr+P/imFoCU0plYvRPlswetsRO78Sckwb4wNl9rsvC2NMSAxAa30IWNXrrneVUg9j/Fn2UnyiShpyvoVJa31lr5sHlVJ3AXcBt8cppIShlJoOPA9UAtcDpxHB8ytRe9p7AdXvPsXJQyYiSCm1VCnV/wcmA3DFI54kcwBIVUpN6XWfnG+DUEqNV0r9Qik1rtfdcq5h/BwCHwCvAFdrrZ1E+PxK1J72OiBdKfU14AGM2SOFGA0hBtYJ/FApVQE8ifHn6g307X2LAWitO5RSzwB3K6U+hzHW+G/AZfGNLGG1AdcA5mBHYSrwXeDBuEYVZ0qpQuBl4Fda65913x/p8yshe9paazdwKXAj0IwxheZKrbU9roElMK31fuA64AdAB/C/wK3BK9hiaJ8DUoEq4AngO1rrD+IbUmLSWvsxZnItwpiL/B7wOHBvPONKAJ8BJgDfV0p19vr3UyJ4fsl2Y0IIkUQSsqcthBBiYJK0hRAiiUjSFkKIJCJJWwghkogkbSGESCKStIUQIolI0hZCiCQiSVsIIZLI/wf+P6mYLZBhmQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e529f39898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(population_x, population_y)\n",
    "\n",
    "\n",
    "xs, ys = draw(100)\n",
    "plt.scatter(xs, ys, s=10)\n",
    "plt.title('Irreducible error');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bias-Variance In Practice\n",
    "\n",
    "In an ideal world, we would minimize the expected prediction error for our model over all input-output points in the population.  However, in practice, we do not know the population data generation process and thus are unable to precisely determine a model's bias, variance, or irreducible error. Instead, we use our observed dataset as an approximation to the population. \n",
    "\n",
    "As we have seen, however, achieving a low training error does not necessarily mean that our model will have a low test error as well. It is easy to obtain a model with extremely low bias and therefore low training error by fitting a curve that passes through every training observation. However, this model will have high variance which typically leads to high test error. Conversely, a model that predicts a constant has low variance but high bias. Fundamentally, this occurs because training error reflects the bias of our model but not the variance; the test error reflects both. In order to minimize test error, our model needs to simultaneously achieve low bias and low variance. To account for this, we need a way to simulate test error without using the test set. This is generally done using cross validation.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Takeaways\n",
    "\n",
    "The bias-variance tradeoff allows us to more precisely describe the modeling phenomena that we have seen thus far.\n",
    "\n",
    "Underfitting is typically caused by too much bias; overfitting is typically caused by too much model variance.\n",
    "\n",
    "Collecting more data reduces variance. For example, the model variance of linear regression goes down by a factor of $ 1\n",
    "/n $, where $ n $ is the number of data points. Thus, doubling the dataset size halves the model variance, and collecting many data points will cause the variance to approach 0. One recent trend is to select a model with low bias and high intrinsic variance (e.g. a neural network) and collect many data points so that the model variance is low enough to make accurate predictions. While effective in practice, collecting enough data for these models tends to require large amounts of time and money.\n",
    "\n",
    "Collecting more data reduces bias if the model can fit the population process exactly. If the model is inherently incapable of modeling the population (as in the example above), even infinite data cannot get rid of model bias.\n",
    "\n",
    "Adding a useful feature to the data, such as a quadratic feature when the underlying process is quadratic, reduces bias. Adding a useless feature rarely increases bias.\n",
    "\n",
    "Adding a feature, whether useful or not, typically increases model variance since each new feature adds a parameter to the model. Generally speaking, models with many parameters have many possible combinations of parameters and therefore have higher variance than models with few parameters. In order to increase a model's prediction accuracy, a new feature should decrease bias more than it increases variance. \n",
    "\n",
    "Removing features will typically increase bias and can cause underfitting. For example, a simple linear model has higher model bias than the same model with a quadratic feature added to it. If the data were generated from a quadratic phenomenon, the simple linear model underfits the data.\n",
    "\n",
    "In the plot below, the X-axis measures model complexity and the Y-axis measures magnitude. Notice  how as model complexity increases, model bias strictly decreases and model variance strictly increases. As we choose more complex models, the test error first decreases then increases as the increased model variance outweighs the decreased model bias.\n",
    "\n",
    "![bias_modeling_bias_var_plot.png](bias_modeling_bias_var_plot.png)\n",
    "\n",
    "As the plot shows, a model with high complexity can achieve low training error but can fail to generalize to the test set because of its high model variance. On the other hand, a model with low complexity will have low model variance but can also fail to generalize because of its high model bias. To select a useful model, we must strike a balance between model bias and variance.\n",
    "\n",
    "As we add more data, we shift the curves on our plot to the right and down, reducing bias and variance:\n",
    "\n",
    "![bias_modeling_bias_var_shiftt.png](bias_modeling_bias_var_shift.png)"
   ]
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    "## Summary\n",
    "\n",
    "The bias-variance tradeoff reveals a fundamental problem in modeling. In order to minimize model risk, we use a combination of feature engineering, model selection, and cross-validation to balance bias and variance."
   ]
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